Coatings of non-planar substrates and methods for the production thereof

ABSTRACT

A coated article is described herein that may comprise a substrate and an optical coating. The substrate may have a major surface comprising a first portion and a second portion. A first direction that is normal to the first portion of the major surface may not be equal to a second direction that is normal to the second portion of the major surface. The optical coating may be disposed on at least the first portion and the second portion of the major surface. The coated article may exhibit at the first portion of the substrate and at the second portion of the substrate hardness of about 8 GPa or greater at an indentation depth of about 50 nm or greater as measured on the anti-reflective surface by a Berkovich Indenter Hardness Test.

CLAIM OF PRIORITY

This application is a continuation application of U.S. patentapplication Ser. No. 15/646,288, filed Jul. 11, 2017, now U.S. Pat. No.10,802,179, which claims the benefit of priority to U.S. ProvisionalApplication Ser. No. 62/360,687 filed on Jul. 11, 2016; the entirecontents of each of these documents are hereby incorporated herein byreference for all purposes.

FIELD

This disclosure relates to durable and/or scratch-resistant articles andmethods for making the same and, more particularly, to durable and/orscratch-resistant optical coatings on non-planar substrates.

TECHNICAL BACKGROUND

Cover articles are often used to protect critical devices withinelectronic products, to provide a user interface for input and/ordisplay, and/or many other functions. Such products include mobiledevices, such as smart phones, mp3 players, and computer tablets. Coverarticles also include architectural articles, transportation articles(e.g., articles used in automotive applications, trains, aircraft, seacraft, etc.), appliance articles, or any article that requires sometransparency, scratch-resistance, abrasion resistance, or a combinationthereof. These applications often demand scratch-resistance and strongoptical performance characteristics, in terms of maximum lighttransmittance and minimum reflectance. Furthermore, some coverapplications require that the color exhibited or perceived, inreflection and/or transmission, does not change appreciably as theviewing angle is changed. In display applications, this is because, ifthe color in reflection or transmission changes with viewing angle to anappreciable degree, the user of the product will perceive a change incolor or brightness of the display, which can diminish the perceivedquality of the display. In other applications, changes in color maynegatively impact the aesthetic requirements or other functionalrequirements.

The optical performance of cover articles can be improved by usingvarious anti-reflective coatings; however known anti-reflective coatingsare susceptible to wear or abrasion. Such abrasion can compromise anyoptical performance improvements achieved by the anti-reflectivecoating. For example, optical filters are often made from multilayercoatings having differing refractive indices and made from opticallytransparent dielectric material (e.g., oxides, nitrides, and fluorides).Most of the typical oxides used for such optical filters are wideband-gap materials, which do not have the requisite mechanicalproperties, such as hardness, for use in mobile devices, architecturalarticles, transportation articles or appliance articles. Nitrides anddiamond-like coatings may exhibit high hardness values but suchmaterials typically do not exhibit the transmittance needed for suchapplications.

Abrasion damage can include reciprocating sliding contact from counterface objects (e.g., fingers). In addition, abrasion damage can generateheat, which can degrade chemical bonds in the film materials and causeflaking and other types of damage to the cover glass. Since abrasiondamage is often experienced over a longer term than the single eventsthat cause scratches, the coating materials disposed experiencingabrasion damage can also oxidize, which further degrades the durabilityof the coating.

Known anti-reflective coatings are also susceptible to scratch damageand, often, even more susceptible to scratch damage than the underlyingsubstrates on which such coatings are disposed. In some instances, asignificant portion of such scratch damage includes microductilescratches, which typically include a single groove in a material havingextended length and with depths in the range from about 100 nm to about500 nm. Microductile scratches may be accompanied by other types ofvisible damage, such as sub-surface cracking, frictive cracking,chipping and/or wear. Evidence suggests that a majority of suchscratches and other visible damage is caused by sharp contact thatoccurs in a single contact event. Once a significant scratch appears onthe cover substrate, the appearance of the article is degraded since thescratch causes an increase in light scattering, which may causesignificant reduction in brightness, clarity and contrast of images onthe display. Significant scratches can also affect the accuracy andreliability of articles including touch sensitive displays. Single eventscratch damage can be contrasted with abrasion damage. Single eventscratch damage is not caused by multiple contact events, such asreciprocating sliding contact from hard counter face objects (e.g.,sand, gravel and sandpaper), nor does it typically generate heat, whichcan degrade chemical bonds in the film materials and cause flaking andother types of damage. In addition, single event scratching typicallydoes not cause oxidization or involve the same conditions that causeabrasion damage and therefore, the solutions often utilized to preventabrasion damage may not also prevent scratches. Moreover, known scratchand abrasion damage solutions often compromise the optical properties.

Some electronics incorporate non-planar cover articles. For example,some smart phone touch screens may be non-planar, where at least aportion of the cover article is curved on its surface. With theincorporation of non-planar articles, optical performance of coatings oncover articles may be altered. For example, a coating will be viewed attwo different angles on different portions of a substrate if thesubstrate is curved. Accordingly, there is a need for non-planar coverarticles, and methods for their manufacture, which are abrasionresistant, scratch-resistant, and/or have improved optical performance.

SUMMARY

According to one embodiment, a coated article may comprise a substrateand an optical coating. The substrate may have a major surfacecomprising a first portion and a second portion. A first direction thatis normal to the first portion of the major surface may not be equal toa second direction that is normal to the second portion of the majorsurface. The angle between the first direction and the second directionmay be in a range of from about 10 degrees to about 180 degrees. Theoptical coating may be disposed on at least the first portion and thesecond portion of the major surface. The optical coating may from ananti-reflective surface. The coated article may exhibit at the firstportion of the substrate and at the second portion of the substratehardness of about 8 GPa or greater at an indentation depth of about 50nm or greater as measured on the anti-reflective surface by a BerkovichIndenter Hardness Test. The coated article may exhibit a single sideaverage light reflectance as measured at the anti-reflective surface atthe first portion of the substrate of about 8% or less, wherein thesingle side average light reflectance of the first portion is measuredat a first incident illumination angle relative to the first direction.The first incident illumination angle may comprise an angle in the rangefrom about 0 degrees to about 60 degrees from the first direction. Thecoated article may exhibit a single-side average light reflectance asmeasured at the anti-reflective surface at the second portion of thesubstrate of about 8% or less, wherein the single side average lightreflectance of the second portion is measured at a second incidentillumination angle relative to the second direction. The second incidentillumination angle may comprises an angle in the range from about 0degrees to about 60 degrees from the second direction. The single sideaverage light reflectance at the first portion and at the second portionmay be measured over an optical wavelength regime in a range of fromabout 400 nm to about 800 nm.

According to another embodiment, a coated article may comprise asubstrate and an optical coating. The substrate may have a major surfacecomprising a first portion and a second portion. A first direction thatis normal to the first portion of the major surface may not be equal toa second direction that is normal to the second portion of the majorsurface. The angle between the first direction and the second directionmay be in a range of from about 10 degrees to about 80 degrees. Theoptical coating may be disposed on at least the first portion and thesecond portion of the major surface. The optical coating may from ananti-reflective surface. The coated article may exhibit at the firstportion of the substrate and at the second portion of the substratehardness of about 8 GPa or greater at an indentation depth of about 50nm or greater as measured on the anti-reflective surface by a BerkovichIndenter Hardness Test. The difference in reflected color of the coatedarticle between the first portion of the substrate and the secondportion of the substrate may be less than or equal to about 10 asmeasured by the reflectance color coordinates in the (L*, a*, b*)colorimetry system under an International Commission on Illuminationilluminant. The difference in reflected color may be defined as√((a*_(first portion)−a*_(second portion))²+(b*_(first portion)−b*_(second portion))²).The reflected color at the first portion may be measured at a firstincident illumination angle relative to the first direction, wherein thefirst incident illumination angle comprises an angle in the range fromabout 0 degrees to about 60 degrees from the first direction. Thereflected color at the second portion may be measured at a secondincident illumination angle relative to the second direction, whereinthe second incident illumination angle comprises an angle in a rangefrom about 0 degrees to about 60 degrees from the second direction.

According to another embodiment, a coated article may comprise asubstrate and an optical coating. The substrate may have a major surfacecomprising a first portion and a second portion. A first direction thatis normal to the first portion of the major surface may not be equal toa second direction that is normal to the second portion of the majorsurface. The angle between the first direction and the second directionmay be in a range of from about 10 degrees to about 180 degrees. Theoptical coating may be disposed on at least the first portion and thesecond portion of the major surface. The optical coating may from ananti-reflective surface. The coated article may exhibit at the firstportion of the substrate and at the second portion of the substratehardness of about 8 GPa or greater at an indentation depth of about 50nm or greater as measured on the anti-reflective surface by a BerkovichIndenter Hardness Test. The difference in reflected color of the coatedarticle between the first portion of the substrate and the secondportion of the substrate may be less than or equal to about 10 asmeasured by the reflectance color coordinates in the (L*, a*, b*)colorimetry system under an International Commission on Illuminationilluminant. The difference in reflected color may be defined as√((a*_(first portion)−a*_(second portion))²+(b*_(first portion)−b*_(second portion))²).The reflected color at the first portion may be measured at a firstincident illumination angle relative to the first direction, wherein thefirst incident illumination angle comprises an angle in the range fromabout 0 degrees to about 60 degrees from the first direction. Thereflected color at the second portion may be measured at a secondincident illumination angle, wherein the second incident illuminationangle may be in a direction equal to the direction of the first incidentillumination angle such that the reflected color at the first portionand at the second portion are measured in the same viewing direction.

According to another embodiment, a coated article may comprise anoptical coating that may comprise a first gradient layer in contact withthe substrate, a scratch-resistant layer over the first gradient layer,and a second gradient layer over the scratch-resistant layer whichdefines the anti-reflective surface. The refractive index of the firstgradient layer at the substrate may be within 0.2 of the refractiveindex of the substrate. The refractive index of the first gradient layerat the scratch-resistant layer may be within 0.2 of the refractive indexof the scratch-resistant layer. The refractive index of the secondgradient layer at the scratch-resistant layer may be within 0.2 of therefractive index of the scratch-resistant layer. The refractive index ofthe second gradient layer at the anti-reflective surface may be fromabout 1.35 to about 1.7.

According to yet another embodiment, a coated article may comprise anoptical coating that may comprise a first anti-reflective coating, ascratch-resistant layer over the first anti-reflective coating, and asecond anti-reflective coating over the scratch-resistant layer whichdefines the anti-reflective surface. The first anti-reflective coatingmay comprise at least a low refractive index (“RI”) layer and a high RIlayer, and the second anti-reflective coating may comprise at least alow RI layer and a high RI layer.

According to yet another embodiment, a coated article may comprise anoptical coating that may comprise a gradient layer in contact with thesubstrate, a scratch-resistant layer over the gradient layer, and ananti-reflective coating over the scratch-resistant layer which definesthe anti-reflective surface. The refractive index of the gradient layerat the substrate may be within 0.2 of the refractive index of thesubstrate. The refractive index of the gradient layer at thescratch-resistant layer may be within 0.2 of the refractive index of thescratch-resistant layer. The anti-reflective coating may comprise atleast a low RI layer and a high RI layer.

According to yet another embodiment, a coated article may comprise anoptical coating that may comprise an anti-reflective coating in contactwith the substrate, a scratch-resistant layer over the first gradientlayer, and a gradient layer over the scratch-resistant layer whichdefines the anti-reflective surface. The anti-reflective coating maycomprise at least a low RI layer and a high RI layer. The refractiveindex of the gradient layer at the scratch-resistant layer may be within0.2 of the refractive index of the scratch-resistant layer. Therefractive index of the second gradient layer at the anti-reflectivesurface may be from about 1.35 to about 1.7.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments as described herein, including the detailed descriptionwhich follows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understanding the natureand character of the claims. The accompanying drawings are included toprovide a further understanding, and are incorporated in and constitutea part of this specification. The drawings illustrate one or moreembodiment(s), and together with the description serve to explainprinciples and operation of the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional side view of a coated article, according toone or more embodiments described herein;

FIG. 2 is a cross-sectional side view of a coated article, according toone or more embodiments described herein;

FIG. 3 is a cross-sectional side view of a coated article, according toone or more embodiments described herein;

FIG. 4 is a cross-sectional side view of a coated article, according toone or more embodiments described herein;

FIG. 5 is a cross-sectional side view of a coated article, according toone or more embodiments described herein;

FIG. 6 is a cross-sectional side view of a coated article, according toone or more embodiments described herein;

FIG. 7 is a cross-sectional side view of a coated article, according toone or more embodiments described herein;

FIG. 8 is a cross-sectional side view of a coated article, according toone or more embodiments described herein;

FIG. 9 depicts a graph of reflectance as a function of wavelength forthe optical coating of Comparative Example A with changing viewingangles relative to normal, according to one or more embodimentsdescribed herein;

FIG. 10 depicts a graph of reflectance as a function of wavelength forthe optical coating of Comparative Example A with changing layerthicknesses as observed at a normal viewing angle, according to one ormore embodiments described herein;

FIG. 11 depicts a graph of reflectance as a function of wavelength forthe optical coatings of Example 1 and Comparative Example B at an 8degree viewing angle relative to normal, according to one or moreembodiments described herein;

FIG. 12 depicts a graph of reflectance as a function of wavelength forthe optical coating of Example 1 as designed and the optical coating ofExample 1 with reduced layer thickness representative of a depositionangle of 35 degrees, as viewed at a normal angle of incidence, accordingto one or more embodiments described herein;

FIG. 13 depicts a graph of a* versus b* in reflectance for L*a*b* colorspace for the optical coating of Example 1 as designed and with reducedlayer thickness representative of an increasing deposition angles, asviewed from a normal angle of incidence to 60 degrees, according to oneor more embodiments described herein;

FIG. 14 depicts a graph of first surface reflectance for the opticalcoating of Example 2 for varying viewing angles, according to one ormore embodiments described herein;

FIG. 15 depicts a graph of a* versus b* of reflected D65 color in L*a*b*color space for the optical coatings of Example 2 having varying topgradient coating thicknesses at different viewing angles, according toone or more embodiments described herein;

FIG. 16 depicts a graph of a* versus b* of transmitted D65 color inL*a*b* color space for the optical coatings of Example 2 having varyingtop gradient coating thicknesses at a normal viewing angle, according toone or more embodiments described herein;

FIG. 17 depicts a graph of the upper gradient layer profiles for thecoating of Example 2, according to one or more embodiments describedherein;

FIG. 18 depicts the hardness profiles of samples prepared as Example 2with varying upper gradient layer thickness, according to one or moreembodiments described herein;

FIG. 19 depicts a graph of the upper gradient layer profiles for thecoating of Example 2 with varying morph parameter, according to one ormore embodiments described herein;

FIG. 20 depicts the hardness profiles of samples prepared as Example 2with varying upper gradient layer morph parameters, according to one ormore embodiments described herein;

FIG. 21 depicts a graph of a* versus b* of reflected D65 color in L*a*b*color space for the optical coatings of Example 2 having varying topgradient morph parameters at different viewing angles, according to oneor more embodiments described herein;

FIG. 22 depicts a graph of a* versus b* of transmitted D65 color inL*a*b* color space for the optical coatings of Example 2 having varyingtop gradient coating morph parameters at a normal viewing angle,according to one or more embodiments described herein;

FIG. 23 graphically depicts the average photopic transmittance and theaverage photopic reflection for the coatings of Example 2 having varyingupper gradient layer MORPH parameters, according to one or moreembodiments described herein;

FIG. 24 graphically depicts the average photopic transmittance and theaverage photopic reflection for the coatings of Example 2 having varyingupper gradient layer thicknesses, according to one or more embodimentsdescribed herein;

FIG. 25 is a cross-sectional side view of an article, according to oneor more embodiments described herein;

FIG. 26 schematically depicts a refractive index profile for a coatedarticle with gradient layers, according to one or more embodimentsdescribed herein;

FIG. 27 schematically depicts a refractive index profile for a coatedarticle with gradient layers, according to one or more embodimentsdescribed herein;

FIG. 28 schematically depicts a refractive index profile for a coatedarticle with gradient layers, according to one or more embodimentsdescribed herein;

FIG. 29 graphically depicts the flow rate of various components as afunction of time for an embodiment of Example 2, according to one ormore embodiments described herein;

FIG. 30 graphically depicts an XPS composition profile for the coatingof FIG. 29 , according to one or more embodiments described herein;

FIG. 31 graphically depicts the calculated refractive index of thecoating of FIG. 29 , according to one or more embodiments describedherein;

FIG. 32 graphically depicts reflectance as a function of wavelength forvarying lower gradient layer thickness, according to one or moreembodiments described herein;

FIG. 33 graphically depicts reflectance as a function of wavelength forvarying lower gradient layer profile shapes, according to one or moreembodiments described herein;

FIGS. 34A and 34B graphically depict reflectance color and transmissioncolor, respectively, as a function of varying upper gradient layerthickness, according to one or more embodiments described herein;

FIG. 35 graphically depicts the 1-surface reflected color of a coatingas a function of top gradient thickness, according to one or moreembodiments described herein;

FIG. 36 graphically depicts the 2-surface reflected color of a coatingas a function of top gradient thickness, according to one or moreembodiments described herein;

FIG. 37 graphically depicts the modulus and hardness of a coating as afunction of top gradient thickness, according to one or more embodimentsdescribed herein;

FIG. 38 graphically depicts the transmitted color of a coating as afunction of top gradient thickness, according to one or more embodimentsdescribed herein;

FIG. 39 graphically depicts the hardness and photopic transmittance ofthe coated article of Example 2

FIG. 40 depicts a graph of reflectance as a function of wavelength forthe optical coating of Example 3 with changing viewing angles relativeto normal, according to one or more embodiments described herein;

FIG. 41 graphically depicts reflectance as a function of wavelength forthe optical coating of Example 4 with changing viewing angles relativeto normal, according to one or more embodiments described herein; and

FIG. 42 graphically depicts a* and b* with varying viewing angles ofincidence for the coating of Examples 3 and 4, according to one or moreembodiments described herein.

FIG. 43A a plan view of an exemplary electronic device incorporating anyof the coated articles disclosed herein.

FIG. 43B is a perspective view of the exemplary electronic device ofFIG. 43A.

DETAILED DESCRIPTION

Reference will now be made in detail to various embodiments of coatedarticles, examples of which are illustrated in the accompanyingdrawings. Referring to FIG. 1 , a coated article 100, according to oneor more embodiments disclosed herein, may include a non-planar substrate110, and an optical coating 120 disposed on the substrate. Thenon-planar substrate 110 may include opposing major surfaces 112, 114and opposing minor surfaces 116, 118. The optical coating 120 is shownin FIG. 1 as being disposed on a first opposing major surface 112;however, the optical coating 120 may be disposed on the second opposingmajor surface 114 and/or one or both of the opposing minor surfaces, inaddition to or instead of being disposed on the first opposing majorsurface 112. The optical coating 120 forms an anti-reflective surface122. The anti-reflective surface 122 forms an air-interface andgenerally defines the edge of the optical coating 120 as well as theedge of the overall coated article 100 The substrate 110 may besubstantially transparent, as described herein.

According to the embodiments described herein, the substrate 110 isnon-planar. As used herein, non-planar substrates refer to substrateswhere at least one of the major surfaces 112, 114 of the substrate 110is not geometrically flat in shape. For example, as shown in FIG. 1 , aportion of major surface 112 may comprise a curved geometry. The degreeof curvature of a major surface 112 may vary. For example, embodimentsmay have a curvature measured by an approximate radius of about 1 mm toseveral meters (i.e., nearly planar), such as from about 3 mm to about30 mm, or from about 5 mm to about 10 mm. In embodiments, the non-planarsubstrate may comprise planar portions, as shown in FIG. 1 . Forexample, a touch screen for a portable electronic device may comprise asubstantially planar surface at or near its center and curved (i.e.,non-planar) portions around its edges. Examples of such substratesinclude the cover glass from an Apple iPhone 6 smartphone or a SamsungGalaxy S6 Edge smartphone. While some embodiments of non-planarsubstrates are depicted, it should be understood that non-planarsubstrates may take on a wide variety of shapes, such as curved sheetsor even tubular sheets.

The non-planar substrate 110 comprises a major surface 112 whichcomprises at least two portions, a first portion 113 and a secondportion 115, which are not flat relative to one another. A direction n₁is normal to the first portion 113 of major surface 112 and a directionn₂ is normal to the second portion 115 of major surface 112. Thedirection n₁ normal to the first portion 113 and the direction n₂ normalto the second portion 115 are not the same. In embodiments, the anglebetween n₁ and n₂ may be at least about 5 degrees, at least about 10degrees, at least about 15 degrees, at least about 20 degrees, at leastabout 25 degrees, at least about 30 degrees, at least about 35 degrees,at least about 40 degrees, at least about 45 degrees, at least about 50degrees, at least about 55 degrees, at least about 60 degrees, at leastabout 70 degrees, at least about 80 degrees, at least about 90 degrees,at least about 120 degrees, at least about 150 degrees, or even leastabout 180 degrees (e.g., the angle between n₁ and n₂ may be 180 degreesfor a tubular substrate. For example, the angle between n₁ and n₂ may bein a range from about 10 degrees to about 30 degrees, from about 10degrees to about 45 degrees, from about 10 degrees to about 60 degrees,from about 10 degrees to about 75 degrees, from about 10 degrees toabout 90 degrees, from about 10 degrees to about 120 degrees, from about10 degrees to about 150 degrees, or from about 10 degrees to about 180degrees. In additional embodiments, the angle between n₁ and n₂ may bein a range from about 10 degrees to about 80 degrees, from about 20degrees to about 80 degrees, from about 30 degrees to about 80 degrees,from about 40 degrees to about 80 degrees, from about 50 degrees toabout 80 degrees, from about 60 degrees to about 80 degrees, from about70 degrees to about 80 degrees, from about 20 degrees to about 180degrees, from about 30 degrees to about 180 degrees, from about 40degrees to about 180 degrees, from about 50 degrees to about 180degrees, from about 60 degrees to about 180 degrees, from about 70degrees to about 150 degrees, or from about 80 degrees to about 180degrees.

Light transmitted through or reflected by the coated article 100 may bemeasured in a viewing direction v (i.e., v₁ for n₁, and v₂ for n₂), asshown in FIG. 1 , which may be non-normal to the major surface 112 ofthe substrate 110. The viewing direction may be referred to as anincident illumination angle as measured from the normal at each surface.For example, and as will be explained herein, reflected color,transmitted color, average light reflectance, average lighttransmission, photopic reflectance, and photopic transmission. Theviewing direction v defines an incident illumination angle θ which isthe angle between the direction normal to a substrate surface n and theviewing direction v (i.e., θ₁ is the incident illumination angle betweennormal direction n₁ and viewing direction v₁, and θ₂ is the incidentillumination angle between normal direction n₂ and viewing direction v₂)It should be understood that while FIG. 1 depicts incident illuminationangles that are not equal to 0 degrees, in some embodiments, theincident illumination angle may be equal to about 0 degrees such thatthe v is equal to n. Optical properties of a portion of the coatedarticle 100 may be different when varying the incident illuminationangle θ.

Still referring to FIG. 1 , in some embodiments, the thickness of theoptical coating 120, as measured in the direction normal to thesubstrate major surface 112, may differ between portions of the opticalcoating 120 disposed over the first portion 113 and the second portion115 of the substrate 110. For example, the optical coating 120 may bedeposited onto the non-planar substrate 110 by a vacuum depositiontechnique such as, for example, chemical vapor deposition (e.g., plasmaenhanced chemical vapor deposition (PECVD), low-pressure chemical vapordeposition, atmospheric pressure chemical vapor deposition, andplasma-enhanced atmospheric pressure chemical vapor deposition),physical vapor deposition (e.g., reactive or nonreactive sputtering orlaser ablation), thermal or e-beam evaporation and/or atomic layerdeposition. Liquid-based methods may also be used such as spraying,dipping, spin coating, or slot coating (for example, using sol-gelmaterials). Generally, vapor deposition techniques may include a varietyof vacuum deposition methods which can be used to produce thin films.For example, physical vapor deposition uses a physical process (such asheating or sputtering) to produce a vapor of material, which is thendeposited on the object which is coated. Such vapor deposition methodsmay utilize a “line-of-sight” deposition scheme, where depositedmaterials move in a uniform direction during deposition onto thesubstrate regardless of the angle between the deposition direction andthe angle normal to the substrate surface.

Referring to FIG. 1 , arrow d shows a line-of-sight depositiondirection. The deposition direction d in FIG. 1 is normal to majorsurface 114 of the substrate 110, such as may be common in a systemwhere the substrate rests on major surface 114 during deposition of theoptical coating 120. The arrow of line d points in the direction of theline-of-sight deposition. Line t shows the direction normal to the majorsurface 112 of the substrate 110. The normal thickness of the opticalcoating 120, as measured in the direction normal to the major surface112 is represented by the length of line t. The deposition angle φ isdefined as the angle between the deposition direction d and thedirection normal to the major surface d. If the optical coating 120 isdeposited with a theoretical line-of-sight deposition, the thickness ofa portion of the optical coating 120 can be determined as the cosine ofφ. Thus, as φ increases, the thickness of the optical coating 120decreases. While the actual thickness of optical coatings 120 depositedby vapor deposition may be different from that determined by the scalarof cosine φ, it provides an estimate useful for modeling optical coatingdesigns which may have good performance when applied onto non-planarsubstrates 110. Additionally, while n₁ and d are in the same directionin FIG. 1 , they need not be in the same direction in all embodiments.

It should be understood that throughout this disclosure, unlessspecified otherwise, thickness of the optical coating 120 is measured inthe normal direction n.

According to embodiments, as described herein, various portions of thecoated article 100 may have optical characteristics such as lightreflectivity, light transmittance, reflective color, and/or transmittedcolor, which appear similar to one another. For example, the opticalcharacteristics at the first portion 113 may be similar to those at thesecond portion 115 when each is viewed in a direction about normal tothe substrate 110 at the respective portion 113, 115 (i.e., _(θ1) isequal to about 0 and _(θ2) is equal to about 0). In other embodiments,the optical characteristics at the first portion 113 may be similar tothose at the second portion 115 when each is viewed at an incidentillumination angle in a specified range relative normal at therespective portion 113, 115 (e.g., _(θ1) is from about 0 degrees toabout 60 degrees and _(θ2) is from about 0 degrees to about 60 degrees).In additional embodiments, the optical characteristics at the firstportion 113 may be similar to those at the second portion 115 when eachis viewed in about the same direction (e.g., the angle between _(v1) and_(v2) is about equal to 0 degrees).

The optical coating 120 includes at least one layer of at least onematerial. The term “layer” may include a single layer or may include oneor more sub-layers. Such sub-layers may be in direct contact with oneanother. The sub-layers may be formed from the same material or two ormore different materials. In one or more alternative embodiments, suchsub-layers may have intervening layers of different materials disposedtherebetween. In one or more embodiments a layer may include one or morecontiguous and uninterrupted layers and/or one or more discontinuous andinterrupted layers (i.e., a layer having different materials formedadjacent to one another). A layer or sub-layers may be formed by anyknown method in the art, including discrete deposition or continuousdeposition processes. In one or more embodiments, the layer may beformed using only continuous deposition processes, or, alternatively,only discrete deposition processes.

The thickness of the optical coating 120 may be about 1 μm or greater inthe direction of deposition while still providing an article thatexhibits the optical performance described herein. In some examples, theoptical coating thickness in the direction of deposition may be in therange from about 1 μm to about 20 μm (e.g., from about 1 μm to about 10μm, or from about 1 μm to about 5 μm).

As used herein, the term “dispose” includes coating, depositing and/orforming a material onto a surface using any known method in the art. Thedisposed material may constitute a layer, as defined herein. The phrase“disposed on” includes the instance of forming a material onto a surfacesuch that the material is in direct contact with the surface and alsoincludes the instance where the material is formed on a surface, withone or more intervening material(s) is between the disposed material andthe surface. The intervening material(s) may constitute a layer, asdefined herein. Additionally, it should be understood that while FIGS.2-8 schematically depict planar substrates, FIGS. 2-8 should beconsidered as having non-planar substrates such as shown in FIG. 1 , andare depicted as planar to simplify the conceptual teachings of therespective figures.

As shown in FIG. 2 , the optical coating 120 may include ananti-reflective coating 130, which may include a plurality of layers(130A, 130B). In one or more embodiments, the anti-reflective coating130 may include a period 132 comprising two or more layers. In one ormore embodiments, the two or more layers may be characterized as havingdifferent refractive indices from each another. In one embodiment, theperiod 132 includes a first low RI layer 130A and a second high RI layer130B. The difference in the refractive index of the first low RI layerand the second high RI layer may be about 0.01 or greater, about 0.05 orgreater, about 0.1 or greater, or even about 0.2 or greater.

As shown in FIG. 2 , the anti-reflective coating 130 may include aplurality of periods 132. A single period 132 may include a first low RIlayer 130A and a second high RI layer 130B, such that when a pluralityof periods 132 are provided, the first low RI layer 130A (designated forillustration as “L”) and the second high RI layer 130B (designated forillustration as “H”) alternate in the following sequence of layers:L/H/L/H or H/L/H/L, such that the first low RI layer 130A and the secondhigh RI layer 130B appear to alternate along the physical thickness ofthe optical coating 120. In the example in FIG. 2 , the anti-reflectivecoating 130 includes three periods 132. In some embodiments, theanti-reflective coating 130 may include up to 25 periods 132. Forexample, the anti-reflective coating 130 may include from about 2 toabout 20 periods 132, from about 2 to about 15 periods 132, from about 2to about 10 periods 132, from about 2 to about 12 periods 132, fromabout 3 to about 8 periods 132, or from about 3 to about 6 periods 132.

In the embodiment shown in FIG. 3 , the anti-reflective coating 130 mayinclude an additional capping layer 131, which may include a lowerrefractive index material than the second high RI layer 130B. In someembodiments, the period 132 may include one or more third layers 130C,as shown in FIG. 3 . The third layer(s) 130C may have a low RI, a highRI or a medium RI. In some embodiments, the third layer(s) 130C may havethe same RI as the first low RI layer 130A or the second high RI layer130B. In other embodiments, the third layer(s) 130C may have a medium RIthat is between the RI of the first low RI layer 130A and the RI of thesecond high RI layer 130B. Alternatively, the third layer(s) 130C mayhave a refractive index greater than the second high RI layer 130B. Thethird layer 130C may be provided in the optical coating 120 in thefollowing exemplary configurations: L_(third layer)/H/L/H/L;H_(third layer)/L/H/L/H; L/H/L/H/L_(third layer);H/L/H/L/H_(third layer); L_(third layer)/H/L/H/L/H_(third layer);H_(third layer)/L/H/L/H/L_(third layer); L_(third layer)/L/H/L/H;H_(third layer)/H/L/H/L; H/L/H/L/L_(third layer);L/H/L/H/H_(third layer); L_(third layer)/L/H/L/H/H_(third layer);H_(third layer)//H/L/H/L/L_(third layer); L/M_(third layer)/H/L/M/H;H/M/L/H/M/L; M/L/H/L/M; as well as other combinations. In theseconfigurations, “L” without any subscript refers to the first low RIlayer and “H” without any subscript refers to the second high RI layer.Reference to “L_(third sub-layer)” refers to a third layer having a lowRI, “H_(third sub-layer)” refers to a third layer having a high RI and“M” refers to a third layer having a medium RI, all relative to thefirst layer and the second layer.

As used herein, the terms “low RI”, “high RI” and “medium RI” refer tothe relative values for the RI to another (e.g., low RI<medium RI<highRI). In one or more embodiments, the term “low RI” when used with thefirst low RI layer or with the third layer, includes a range from about1.3 to about 1.7 or 1.75. In one or more embodiments, the term “high RI”when used with the second high RI layer or with the third layer,includes a range from about 1.7 to about 2.5 (e.g., about 1.85 orgreater). In some embodiments, the term “medium RI” when used with thethird layer, includes a range from about 1.55 to about 1.8. In someinstances, the ranges for low RI, high RI, and medium RI may overlap;however, in most instances, the layers of the anti-reflective coating130 have the general relationship regarding RI of: low RI<medium RI<highRI.

The third layer(s) 130C may be provided as a separate layer from aperiod 132 and may be disposed between the period 132 or plurality ofperiods 132 and the capping layer 131, as shown in FIG. 4 . The thirdlayer(s) may also be provided as a separate layer from a period 132 andmay be disposed between the substrate 110 and the plurality of periods132, as shown in FIG. 5 . The third layer(s) 130C may be used inaddition to an additional coating 140 instead of the capping layer 131or in addition to the capping layer 131, as shown in FIG. 6 .

Materials suitable for use in the anti-reflective coating 130 include:SiO₂, Al₂O₃, GeO₂, SiO, AlOxNy, AlN, SiNx, SiO_(x)N_(y),Si_(u)Al_(v)O_(x)N_(y), Ta₂O₅, Nb₂O₅, TiO₂, ZrO₂, TiN, MgO, MgF₂,BaF₂,CaF₂, SnO₂, HfO₂, Y₂O₃, MoO₃, DyF₃, YbF₃, YF₃, CeF₃, polymers,fluoropolymers, plasma-polymerized polymers, siloxane polymers,silsesquioxanes, polyimides, fluorinated polyimides, polyetherimide,polyethersulfone, polyphenylsulfone, polycarbonate, polyethyleneterephthalate, polyethylene naphthalate, acrylic polymers, urethanepolymers, polymethylmethacrylate, other materials cited below assuitable for use in a scratch-resistant layer, and other materials knownin the art. Some examples of suitable materials for use in the first lowRI layer include SiO₂, Al₂O₃, GeO₂, SiO, AlO_(x)N_(y), SiO_(x)N_(y),Si_(u)Al_(v)O_(x)N_(y), MgO, MgAl₂O₄, MgF₂, BaF₂, CaF₂, DyF₃, YbF₃, YF₃,and CeF₃. The nitrogen content of the materials for use in the first lowRI layer may be minimized (e.g., in materials such as Al₂O₃ andMgAl₂O₄). Some examples of suitable materials for use in the second highRI layer include Si_(u)Al_(v)O_(x)N_(y), Ta₂O₅, Nb₂O₅, AlN, Si₃N₄,AlO_(x)N_(y), SiO_(x)N_(y), SiN_(x), SiN_(x):H_(y), HfO₂, TiO₂, ZrO₂,Y₂O₃, Al₂O₃, MoO₃ and diamond-like carbon. In examples, the high RIlayer may also be a high hardness layer or a scratch-resistant layer,and the high RI materials listed above may also comprise high hardnessor scratch resistance. The oxygen content of the materials for thesecond high RI layer and/or the scratch-resistant layer may beminimized, especially in SiN_(x) or AlN_(x) materials. AlO_(x)N_(y)materials may be considered to be oxygen-doped AlN_(x), that is they mayhave an AlN_(x) crystal structure (e.g. wurtzite) and need not have anAlON crystal structure. Exemplary AlO_(x)N_(y) high RI materials maycomprise from about 0 atom % to about 20 atom % oxygen, or from about 5atom % to about 15 atom % oxygen, while including 30 atom % to about 50atom % nitrogen. Exemplary Si_(u)Al_(v)O_(x)N_(y) high RI materials maycomprise from about 10 atom % to about 30 atom % or from about 15 atom %to about 25 atom % silicon, from about 20 atom % to about 40 atom % orfrom about 25 atom % to about 35 atom % aluminum, from about 0 atom % toabout 20 atom % or from about 1 atom % to about 20 atom % oxygen, andfrom about 30 atom % to about 50 atom % nitrogen. The foregoingmaterials may be hydrogenated up to about 30% by weight. Where amaterial having a medium refractive index is desired, some embodimentsmay utilize AlN and/or SiO_(x)N_(y). The hardness of the second high RIlayer and/or the scratch-resistant layer may be characterizedspecifically. In some embodiments, the maximum hardness of the secondhigh RI layer and/or a scratch-resistant layer, as measured by theBerkovich Indenter Hardness Test, may be about 8 GPa or greater, about10 GPa or greater, about 12 GPa or greater, about 15 GPa or greater,about 18 GPa or greater, or about 20 GPa or greater. In some cases, thesecond high RI layer material may be deposited as a single layer and maybe characterized as a scratch-resistant layer, and this single layer mayhave a thickness between about 500 and 2000 nm for repeatable hardnessdetermination.

In one or more embodiments, at least one of the layer(s) of theanti-reflective coating 130 may include a specific optical thicknessrange. As used herein, the term “optical thickness” is determined by thesum of the physical thickness and the refractive index of a layer. Inone or more embodiments, at least one of the layers of theanti-reflective coating 130 may include an optical thickness in therange from about 2 nm to about 200 nm, from about 10 nm to about 100 nm,from about 15 nm to about 100 nm, from about 15 to about 500 nm, or fromabout 15 to about 5000 nm. In some embodiments, all of the layers in theanti-reflective coating 130 may each have an optical thickness in therange from about 2 nm to about 200 nm, from about 10 nm to about 100 nm,from about 15 nm to about 100 nm, from about 15 to about 500 nm, or fromabout 15 to about 5000 nm. In some cases, at least one layer of theanti-reflective coating 130 has an optical thickness of about 50 nm orgreater. In some cases, each of the first low RI layers have an opticalthickness in the range from about 2 nm to about 200 nm, from about 10 nmto about 100 nm, from about 15 nm to about 100 nm, from about 15 toabout 500 nm, or from about 15 to about 5000 nm. In other cases, each ofthe second high RI layers have an optical thickness in the range fromabout 2 nm to about 200 nm, from about 10 nm to about 100 nm, from about15 nm to about 100 nm, from about 15 to about 500 nm, or from about 15to about 5000 nm. In yet other cases, each of the third layers have anoptical thickness in the range from about 2 nm to about 200 nm, fromabout 10 nm to about 100 nm, from about 15 nm to about 100 nm, fromabout 15 to about 500 nm, or from about 15 to about 5000 nm.

In some embodiments, the top-most air-side layer may comprise a high RIlayer that also exhibits high hardness. In some embodiments, anadditional coating 140 may be disposed on top of this top-most air-sidehigh RI layer (e.g., the additional coating may include a low-frictioncoating, an oleophobic coating, or an easy-to-clean coating). Theaddition of a low RI layer having a very low thickness (e.g., about 10nm or less, about 5 nm or less or about 2 nm or less) has minimalinfluence on the optical performance, when added to the top-mostair-side layer comprising a high RI layer. The low RI layer having avery low thickness may include SiO₂, an oleophobic or low-frictionlayer, or a combination of SiO₂ and an oleophobic material. Exemplarylow-friction layers may include diamond-like carbon, such materials (orone or more layers of the optical coating) may exhibit a coefficient offriction less than 0.4, less than 0.3, less than 0.2, or even less than0.1.

In one or more embodiments, the anti-reflective coating 130 may have aphysical thickness of about 800 nm or less. The anti-reflective coating130 may have a physical thickness in the range from about 10 nm to about800 nm, from about 50 nm to about 800 nm, from about 100 nm to about 800nm, from about 150 nm to about 800 nm, from about 200 nm to about 800nm, from about 10 nm to about 750 nm, from about 10 nm to about 700 nm,from about 10 nm to about 650 nm, from about 10 nm to about 600 nm, fromabout 10 nm to about 550 nm, from about 10 nm to about 500 nm, fromabout 10 nm to about 450 nm, from about 10 nm to about 400 nm, fromabout 10 nm to about 350 nm, from about 10 nm to about 300 nm, fromabout 50 to about 300, and all ranges and sub-ranges therebetween.

In one or more embodiments, the combined physical thickness of thesecond high RI layer(s) may be characterized. For example, in someembodiments, the combined thickness of the second high RI layer(s) maybe about 100 nm or greater, about 150 nm or greater, about 200 nm orgreater, or even about 500 nm or greater. The combined thickness is thecalculated combination of the thicknesses of the individual high RIlayer(s) in the anti-reflective coating 130, even when there areintervening low RI layer(s) or other layer(s). In some embodiments, thecombined physical thickness of the second high RI layer(s), which mayalso comprise a high-hardness material (e.g., a nitride or an oxynitridematerial), may be greater than 30% of the total physical thickness ofthe anti-reflective coating. For example, the combined physicalthickness of the second high RI layer(s) may be about 40% or greater,about 50% or greater, about 60% or greater, about 70% or greater, about75% or greater, or even about 80% or greater, of the total physicalthickness of the anti-reflective coating. Additionally or alternatively,the amount of the high refractive index material, which may also be ahigh-hardness material, included in the optical coating may becharacterized as a percentage of the physical thickness of the uppermost (i.e., user side or side of the optical coating opposite thesubstrate) 500 nm of the article or optical coating 120. Expressed as apercentage of the upper most 500 nm of the article or optical coating,the combined physical thickness of the second high RI layer(s) (or thethickness of the high refractive index material) may be about 50% orgreater, about 60% or greater, about 70% or greater, about 80% orgreater, or even about 90% or greater. In some embodiments, greaterproportions of hard and high-index material within the anti-reflectivecoating can also simultaneously be made to also exhibit low reflectance,low color, and high abrasion resistance as further described elsewhereherein. In one or more embodiments, the second high RI layers mayinclude a material having a refractive index greater than about 1.85 andthe first low RI layers may include a material having a refractive indexless than about 1.75. In some embodiments, the second high RI layers mayinclude a nitride or an oxynitride material. In some instances, thecombined thickness of all the first low RI layers in the optical coating(or in the layers that are disposed on the thickest second high RI layerof the optical coating) may be about 200 nm or less (e.g., about 150 nmor less, about 100 nm or less, about 75 nm or less, or about 50 nm orless).

The coated article 100 may include one or more additional coatings 140disposed on the anti-reflective coating, as shown in FIG. 6 . In one ormore embodiments, the additional coating may include an easy-to-cleancoating. An example of a suitable an easy-to-clean coating is describedin U.S. patent application Ser. No. 13/690,904, entitled “PROCESS FORMAKING OF GLASS ARTICLES WITH OPTICAL AND EASY-TO-CLEAN COATINGS,” filedon Nov. 30, 2012, which is incorporated herein in its entirety byreference. The easy-to-clean coating may have a thickness in the rangefrom about 5 nm to about 50 nm and may include known materials such asfluorinated silanes. The easy-to-clean coating may alternately oradditionally comprise a low-friction coating or surface treatment.Exemplary low-friction coating materials may include diamond-likecarbon, silanes (e.g. fluorosilanes), phosphonates, alkenes, andalkynes. In some embodiments, the easy-to-clean coating may have athickness in the range from about 1 nm to about 40 nm, from about 1 nmto about 30 nm, from about 1 nm to about 25 nm, from about 1 nm to about20 nm, from about 1 nm to about 15 nm, from about 1 nm to about 10 nm,from about 5 nm to about 50 nm, from about 10 nm to about 50 nm, fromabout 15 nm to about 50 nm, from about 7 nm to about 20 nm, from about 7nm to about 15 nm, from about 7 nm to about 12 nm or from about 7 nm toabout 10 nm, and all ranges and sub-ranges therebetween.

The additional coating 140 may include a scratch-resistant layer orlayers. In some embodiments, the additional coating 140 includes acombination of easy-to-clean material and scratch-resistant material. Inone example, the combination includes an easy-to-clean material anddiamond-like carbon. Such additional coatings 140 may have a thicknessin the range from about 5 nm to about 20 nm. The constituents of theadditional coating 140 may be provided in separate layers. For example,the diamond-like carbon may be disposed as a first layer and the easy-toclean can be disposed as a second layer on the first layer ofdiamond-like carbon. The thicknesses of the first layer and the secondlayer may be in the ranges provided above for the additional coating.For example, the first layer of diamond-like carbon may have a thicknessof about 1 nm to about 20 nm or from about 4 nm to about 15 nm (or morespecifically about 10 nm) and the second layer of easy-to-clean may havea thickness of about 1 nm to about 10 nm (or more specifically about 6nm). The diamond-like coating may include tetrahedral amorphous carbon(Ta—C), Ta—C:H, and/or a-C—H.

As mentioned herein, the optical coating 120 may include ascratch-resistant layer 150, which may be disposed between theanti-reflective coating 130 and the substrate 110. In some embodiment,the scratch-resistant layer 150 is disposed between the layers of theanti-reflective coating 130 (such as 150 as shown in FIG. 7 ). The twosections of the anti-reflective coating (i.e., a first section disposedbetween the scratch-resistant layer 150 and the substrate 110, and asecond section disposed on the scratch-resistant layer) may have adifferent thickness from one another or may have essentially the samethickness as one another. The layers of the two sections of theanti-reflective coating 130 may be the same in composition, order,thickness and/or arrangement as one another or may differ from oneanother.

Exemplary materials used in the scratch-resistant layer 150 (or thescratch-resistant layer used as an additional coating 140) may includean inorganic carbide, nitride, oxide, diamond-like material, orcombination of these. Examples of suitable materials for thescratch-resistant layer 150 include metal oxides, metal nitrides, metaloxynitride, metal carbides, metal oxycarbides, and/or combinationsthereof. Exemplary metals include B, Al, Si, Ti, V, Cr, Y, Zr, Nb, Mo,Sn, Hf, Ta and W. Specific examples of materials that may be utilized inthe scratch-resistant layer 150 or coating may include Al₂O₃, AlN,AlO_(x)N_(y), Si₃N₄, SiO_(x)N_(y), Si_(u)Al_(v)O_(x)N_(y), diamond,diamond-like carbon, Si_(x)C_(y), Si_(x)O_(y)C_(z), ZrO₂, TiO_(x)N_(y)and combinations thereof. The scratch-resistant layer 150 may alsocomprise nanocomposite materials, or materials with a controlledmicrostructure to improve hardness, toughness, or abrasion/wearresistance. For example the scratch-resistant layer 150 may comprisenanocrystallites in the size range from about 5 nm to about 30 nm. Inembodiments, the scratch-resistant layer 150 may comprisetransformation-toughened zirconia, partially stabilized zirconia, orzirconia-toughened alumina. In embodiments, the scratch-resistant layer150 exhibits a fracture toughness value greater than about 1 MPa√m andsimultaneously exhibits a hardness value greater than about 8 GPa.

The scratch-resistant layer 150 may include a single layer (as shown inFIG. 7 ), or multiple sub-layers or single layers that exhibit arefractive index gradient. Where multiple layers are used, such layersform a scratch-resistant coating. For example, a scratch-resistant layer150 may include a compositional gradient of Si_(u)Al_(v)O_(x)N_(y) wherethe concentration of any one or more of Si, Al, O and N are varied toincrease or decrease the refractive index. The refractive index gradientmay also be formed using porosity. Such gradients are more fullydescribed in U.S. patent application Ser. No. 14/262,224, entitled“Scratch-Resistant Articles with a Gradient Layer”, filed on Apr. 28,2014, which is hereby incorporated by reference in its entirety.

In one embodiment, depicted in FIG. 8 , the optical coating 120 maycomprise a scratch-resistant layer 150 that is integrated as a high RIlayer, and one or more low RI layers 130A and high RI layers 130B may bepositioned over the scratch-resistant layer 150, with an optionalcapping layer 131 positioned over the low RI layers 130A and high RIlayers 130B, where the capping layer 131 comprises a low RI material.The scratch-resistant layer 150 may be alternately defined as thethickest hard layer or the thickest high RI layer in the overall opticalcoating 120 or in the overall coated article 100. Without being bound bytheory, it is believed that the coated article 100 may exhibit increasedhardness at indentation depths when a relatively thin amount of materialis deposited over the scratch-resistant layer 150. However, theinclusion of low RI and high RI layers over the scratch-resistant layer150 may enhance the optical properties of the coated article 100. Insome embodiments, relatively few layers (e.g., only 1, 2, 3, 4, or 5layers) may positioned over the scratch-resistant layer 150 and theselayers may each be relatively thin (e.g. less than 100 nm, less than 75nm, less than 50 nm, or even less than 25 nm).

In embodiments, the layers deposited over the scratch-resistant layer150 (i.e., on the air side of the scratch-resistant layer 150) may havea total thickness (i.e., in combination) of less than or equal to about1000 nm, less than or equal to about 500 nm, less than or equal to about450 nm, less than or equal to about 400 nm, less than or equal to about350 nm, less than or equal to about 300 nm, less than or equal to about250 nm, less than or equal to about 225 nm, less than or equal to about200 nm, less than or equal to about 175 nm, less than or equal to about150 nm, less than or equal to about 125 nm, less than or equal to about100 nm, less than or equal to about 90 nm, less than or equal to about80 nm, less than or equal to about 70 nm, less than or equal to about 60nm, or even less than or equal to about 50 nm.

In embodiments, the total thickness of low RI layer(s) (the sum ofthickness of all low RI layers, even if they are not in contact) thatare positioned over the scratch-resistant layer 150 (i.e., on the airside of the scratch-resistant layer 150) may be less than or equal toabout 500 nm, less than or equal to about 450 nm, less than or equal toabout 400 nm, less than or equal to about 350 nm, less than or equal toabout 300 nm, less than or equal to about 250 nm, less than or equal toabout 225 nm, less than or equal to about 200 nm, less than or equal toabout 175 nm, less than or equal to about 150 nm, less than or equal toabout 125 nm, less than or equal to about 100 nm, less than or equal toabout 90 nm, less than or equal to about 80 nm, less than or equal toabout 70 nm, less than or equal to about 60 nm, less than or equal toabout 50 nm, less than or equal to about 40 nm, less than or equal toabout 30 nm, less than or equal to about 20 nm, or even less than orequal to about 10 nm.

In one or more embodiments, the optical coating 120 may comprise one ormore gradient layers, which each may comprise a compositional gradientalong their respective thicknesses, as shown in FIG. 25 . In oneembodiment, the optical coating 120 may comprise a lower gradient layer170, a scratch-resistant layer 150 (as described above), and an uppergradient layer 160. The lower gradient layer 170 may be positioned indirect contact with the substrate 110. The scratch-resistant layer 150may be over the lower gradient layer 170, and the upper gradient layermay be in direct contact and over the scratch-resistant layer 150. Thescratch-resistant layer 150 may comprise one or more relatively hardmaterials with high refractive indices, such as SiN_(x), SiAlON, SiON,etc. In embodiments, the thickness of the scratch-resistant layer 150may be from about 200 nm to several microns, such as is described withreference to the scratch-resistant layer 150 in other embodiments. Thelower gradient layer 170 may have a refractive index which varies fromabout the refractive index of the substrate (which may be relativelylow) in portions which contact the substrate 110 to the refractive indexof the scratch-resistant layer 150 (which may be relatively high) inportions that contact the scratch-resistant layer 150. The lowergradient layer 170 may have a thickness of from about 10 nm to severalmicrons, such as 50 nm to 1000 nm, 100 nm to 1000 nm, or 500 nm to 1000nm. The upper gradient layer 160 may have a refractive index whichvaries from about the refractive index of the scratch-resistant layer150 (which may be relatively high) at portions which contact thescratch-resistant layer 150 to a relatively low refractive index at theair interface at the anti-reflective surface 122. The uppermost portionof the upper gradient layer 160 (at the anti-reflective surface 122) maycomprise materials with a refractive index of 1.38 to 1.55, such as, butnot limited to, silicate glass, silica, phosphorous glass, or magnesiumfluoride. The uppermost portion of the upper gradient layer 160 may alsocomprise material with a refractive index from about 1.38 to 1.7 and anengineered hardness, such as, but not limited to, Al₂O₃,Si_(u)Al_(v)O_(x), Si_(u)Al_(v)O_(x)N_(y), Si_(v)O_(x)N_(y), orAl_(v)O_(x)N_(y). High hardness and low refractive index may bedesirable at the anti-reflective surface 122. FIG. 26 depicts an examplerefractive index profile of an optical coating 120 of FIG. 25 . Thesubstrate 110, lower gradient layer 170, scratch-resistant layer 150,and upper gradient layer 160 are marked in their corresponding portionson the refractive index profile of FIG. 26 .

In one or more embodiments, the refractive index of the lower gradientlayer 170 at the substrate 110 may be within 0.2 (such as within 0.15,0.1, 0.05, 0.02, or 0.01) of the refractive index of the substrate 110.The refractive index of the lower gradient layer 170 at thescratch-resistant layer may be within 0.2 (such as within 0.15, 0.1,0.05, 0.02, or 0.01) of the refractive index of the scratch-resistantlayer 150. The refractive index of the upper gradient layer 160 at thescratch-resistant layer 150 may be within 0.2 (such as within 0.15, 0.1,0.05, 0.02, or 0.01) of the refractive index of the scratch-resistantlayer 150. The refractive index of the upper gradient layer 160 at theanti-reflective surface 122 may be from about 1.38 to about 1.55. Inembodiments, the refractive index of the scratch-resistant layer 150 maybe at least about 1.75, 1.8, or even 1.9.

In one or more embodiments, the lower gradient layer 170, the uppergradient layer 160, or both, may have a non-linear concentration profile(resulting in a non-linear refractive index profile). For example, FIGS.27 and 28 depict non-linear upper gradient layers 160. Such non-linearupper gradient layers 160 may be quantified by a morph parameter, aswill be described in the examples which follow. A morph parameter of 1corresponds to a linear refractive index profile. A morph parameter ofless than 1 refers to a non-linear refractive index profile where therefractive index of the gradient layer at its geometric midpoint isgreater than the average of the refractive indices at the upper andlower surfaces of the gradient layer. FIG. 27 shows the upper gradientlayer 160 with a morph parameter of less than 1. A morph parameter ofgreater than 1 refers to a non-linear refractive index profile where therefractive index of the gradient layer at its midpoint is less than theaverage of the refractive indices at the upper and lower surfaces of thegradient layer. FIG. 28 shows the upper gradient layer 160 with a morphparameter of greater than 1. Coated articles 100 with morph parametersof less than 1 may have increased hardness due to the higherconcentration of hard materials throughout the gradient layer.

According to one or more embodiments, the coated article 100 may includea structure that is a hybrid between the gradient-including structure ofFIG. 26 and the alternating high RI/low RI-including structure of FIG. 7. For example, in FIG. 7 the scratch-resistant layer is sandwiched bytwo anti-reflective coatings 130 which have alternating high RI/low RIlayers, and FIG. 26 replaces those alternating high RI/low RI layerswith gradient layers. A hybrid coating may include a gradient layerbelow the scratch-resistant layer and an alternating high RI/low RIcoating over the scratch-resistant layer. In an alternative embodiment,a hybrid coating may include a gradient layer over the scratch-resistantlayer and an alternating high RI/low RI coating below thescratch-resistant layer. It should be understood that the teachingpresented herein regarding gradient layer-including embodiments andalternating high RI/low RI layer coating embodiments (sometimes referredto as anti-reflective coating embodiments) may be combined andinterchanged to produce hybrids of the two designs.

The optical coating 120 and/or the coated article 100 may be describedin terms of a hardness measured by a Berkovich Indenter Hardness Test.As used herein, the “Berkovich Indenter Hardness Test” includesmeasuring the hardness of a material on a surface thereof by indentingthe surface with a diamond Berkovich indenter. The Berkovich IndenterHardness Test includes indenting the anti-reflective surface 122 of thecoated article 100 or the surface of any one or more of the layers inthe optical coating 120 with the diamond Berkovich indenter to form anindent to an indentation depth in the range from about 50 nm to about1000 nm (or the entire thickness of the optical coating 120 or layerthereof, whichever is less) and measuring the maximum hardness from thisindentation along the entire indentation depth range or a segment ofthis indentation depth (e.g., in the range from about 100 nm to about600 nm), generally using the methods set forth in Oliver, W. C.; Pharr,G. M. An improved technique for determining hardness and elastic modulususing load and displacement sensing indentation experiments. J. Mater.Res., Vol. 7, No. 6, 1992, 1564-1583; and Oliver, W. C.; Pharr, G. M.Measurement of Hardness and Elastic Modulus by Instrument Indentation:Advances in Understanding and Refinements to Methodology. J. Mater.Res., Vol. 19, No. 1, 2004, 3-20. As used herein, hardness refers to amaximum hardness, and not an average hardness.

Typically, in nanoindentation measurement methods (such as by using aBerkovich indenter) of a coating that is harder than the underlyingsubstrate, the measured hardness may appear to increase initially due todevelopment of the plastic zone at shallow indentation depths and thenincreases and reaches a maximum value or plateau at deeper indentationdepths. Thereafter, hardness begins to decrease at even deeperindentation depths due to the effect of the underlying substrate. Wherea substrate having an increased hardness compared to the coating isutilized, the same effect can be seen; however, the hardness increasesat deeper indentation depths due to the effect of the underlyingsubstrate.

The indentation depth range and the hardness values at certainindentation depth range(s) can be selected to identify a particularhardness response of the optical film structures and layers thereof,described herein, without the effect of the underlying substrate. Whenmeasuring hardness of the optical film structure (when disposed on asubstrate) with a Berkovich indenter, the region of permanentdeformation (plastic zone) of a material is associated with the hardnessof the material. During indentation, an elastic stress field extendswell beyond this region of permanent deformation. As indentation depthincreases, the apparent hardness and modulus are influenced by stressfield interactions with the underlying substrate. The substrateinfluence on hardness occurs at deeper indentation depths (i.e.,typically at depths greater than about 10% of the optical film structureor layer thickness). Moreover, a further complication is that thehardness response requires a certain minimum load to develop fullplasticity during the indentation process. Prior to that certain minimumload, the hardness shows a generally increasing trend.

At small indentation depths (which also may be characterized as smallloads) (e.g., up to about 50 nm), the apparent hardness of a materialappears to increase dramatically versus indentation depth. This smallindentation depth regime does not represent a true metric of hardnessbut instead, reflects the development of the aforementioned plasticzone, which is related to the finite radius of curvature of theindenter. At intermediate indentation depths, the apparent hardnessapproaches maximum levels. At deeper indentation depths, the influenceof the substrate becomes more pronounced as the indentation depthsincrease. Hardness may begin to drop dramatically once the indentationdepth exceeds about 30% of the optical coating 120 thickness or thelayer thickness.

In some embodiments, the coated article 100 may exhibit a hardness ofabout 8 GPa or greater, about 10 GPa or greater, or about 12 GPa orgreater (e.g., about 14 GPa or greater, about 16 GPa or greater, about18 GPa or greater, or about 20 GPa or greater) when measured at theanti-reflective surface 122. The hardness of the coated article 100 mayeven be up to about 20 GPa or 30 GPa. Such measured hardness values maybe exhibited by the optical coating 120 and/or the coated article 100along an indentation depth of about 50 nm or greater or about 100 nm orgreater (e.g., from about 50 nm to about 300 nm, from about 50 nm toabout 400 nm, from about 50 nm to about 500 nm, from about 50 nm toabout 600 nm, from about 200 nm to about 300 nm, from about 200 nm toabout 400 nm, from about 200 nm to about 500 nm, or from about 200 nm toabout 600 nm). In one or more embodiments, the article exhibits ahardness that is greater than the hardness of the substrate (which canbe measured on the opposite surface from the anti-reflective surface).

According to embodiments, the hardness may be measured at differentportions of the coated article 100. For example, the coated article mayexhibit a hardness of at least 8 GPa or greater at an indentation depthof at least about 50 nm or greater at the anti-reflective surface 122 atthe first portion 113 and at the second portion 115. For example, thehardness at the first portion 113 and at second portion 115 may be about8 GPa or greater, about 10 GPa or greater, or about 12 GPa or greater(e.g., about 14 GPa or greater, about 16 GPa or greater, about 18 GPa orgreater, or about 20 GPa or greater).

According to embodiments, the coated articles described herein may havedesirable optical properties (such as low reflectance and neutral color)at various portions of the coated article 100, such as the first portion113 and the second portion 115. For example, light reflectance may berelatively low (and transmittance may be relatively high) at the firstportion 113 and at the second portion 115 when each is viewed at anincident illumination angle near normal to the respective portions. Inanother embodiment, when each portion is viewed at a near normalincident illumination angle, the difference in color between the twoportions may be insignificant to the naked eye. In another embodiment,when the portions are viewed at incident illumination angles that havethe same direction, the color may be insignificant to the naked eye andthere may be relatively low reflectance at each portion (i.e., theincident illumination angles relative to the surfaces of each portionare different because the portions are at an angle to one another, butthe illumination direction is the same. Optical properties may includeaverage light transmittance, average light reflectance, photopicreflectance, photopic transmittance, reflected color (i.e., in L*a*b*color coordinates), and transmitted color (i.e., in L*a*b* colorcoordinates).

As used herein, the term “transmittance” is defined as the percentage ofincident optical power within a given wavelength range transmittedthrough a material (e.g., the article, the substrate or the optical filmor portions thereof). The term “reflectance” is similarly defined as thepercentage of incident optical power within a given wavelength rangethat is reflected from a material (e.g., the article, the substrate, orthe optical film or portions thereof). Reflectance may be measured as asingle side reflectance when measured at the anti-reflective surface 122only (e.g., when removing the reflections from an uncoated back surface(e.g., 114 in FIG. 1 ) of the article, such as through usingindex-matching oils on the back surface coupled to an absorber, or otherknown methods). In one or more embodiments, the spectral resolution ofthe characterization of the transmittance and reflectance is less than 5nm or 0.02 eV. The color may be more pronounced in reflection. Theangular color shifts in reflection with viewing angle due to a shift inthe spectral reflectance oscillations with incident illumination angle.Angular color shifts in transmittance with viewing angle are also due tothe same shift in the spectral transmittance oscillation with incidentillumination angle. The observed color and angular color shifts withincident illumination angle are often distracting or objectionable todevice users, particularly under illumination with sharp spectralfeatures such as fluorescent lighting and some LED lighting. Angularcolor shifts in transmission may also play a factor in color shift inreflection and vice versa. Factors in angular color shifts intransmission and/or reflection may also include angular color shifts dueto viewing angle or angular color shifts away from a certain white pointthat may be caused by material absorption (somewhat independent ofangle) defined by a particular illuminant or test system.

The average light reflectance and average light transmittance may bemeasured over a wavelength regime of from about 400 nm to about 800 nm.In additional embodiments, the optical wavelength regime may comprisewavelength ranges such as from about 450 nm to about 650 nm, from about420 nm to about 680 nm, from about 420 nm to about 700 nm, from about420 nm to about 740 nm, from about 420 nm to about 850 nm, or from about420 nm to about 950 nm.

The coated article 100 may also be characterized by is photopictransmittance and reflectance at various portions. As used herein,photopic reflectance mimics the response of the human eye by weightingthe reflectance versus wavelength spectrum according to the human eye'ssensitivity. Photopic reflectance may also be defined as the luminance,or tristimulus Y value of reflected light, according to knownconventions such as CIE color space conventions. The average photopicreflectance is defined in the below equation as the spectralreflectance, R(λ) multiplied by the illuminant spectrum, I(λ) and theCIE's color matching function y(λ), related to the eye's spectralresponse:

$\left\langle R_{p} \right\rangle = {\int_{380{nm}}^{720{nm}}{{R(\lambda)} \times {I(\lambda)} \times {\overset{¯}{y}(\lambda)}d\lambda}}$

The average photopic transmittance is defined in the below equation asthe spectral transmittance, T(λ) multiplied by the illuminant spectrum,I(λ) and the CIE's color matching function y(λ), related to the eye'sspectral response:

$\left\langle T_{p} \right\rangle = {\int_{380{nm}}^{720{nm}}{{T(\lambda)} \times {I(\lambda)} \times {\overset{¯}{y}(\lambda)}d\lambda}}$

According to one embodiment, the coated article 100 may exhibit a singleside average light reflectance as measured at the anti-reflectivesurface 122 at the first portion 113 of the substrate 110 of about 8% orless, wherein the single side average light reflectance of the firstportion 113 is measured at a first incident illumination angle θ₁relative to n₁, and wherein the first incident illumination angle θ₁comprises an angle in the range from about 0 degrees to about 60 degreesfrom the n₁. In additional embodiments, the first incident illuminationangle θ₁ may comprise angles in the range from about 0 degrees to about60, from about 0 degrees to about 50, from about 0 degrees to about 40,from about 0 degrees to about 30, from about 0 degrees to about 20, orfrom about 0 degrees to about 10 from n₁. In additional embodiments, thecoated article 100 may exhibit a single side average light reflectanceas measured at the anti-reflective surface 122 at the first portion 113of the substrate 110 of about 8% or less for all incident illuminationangles θ₁ in a range from about 0 degrees to about 60 degrees, fromabout 0 degrees to about 50, from about 0 degrees to about 40, fromabout 0 degrees to about 30, from about 0 degrees to about 20, or fromabout 0 degrees to about 10 from n₁. In additional embodiments, givenany of the described ranges of incident illumination angles θ₁, thesingle side average light reflectance as measured at the anti-reflectivesurface 122 at the first portion 113 of the substrate 110 may be about10% or less, about 9% or less, about 8% or less, about 7% or less, about6% or less, about 5% or less, about 4% or less, about 3% or less, about2% or less, about 1% or less, or about 0.8% or less over the opticalwavelength regime. For example, the single side average lightreflectance may be in the range from about 0.4% to about 9%, from about0.4% to about 8%, from about 0.4% to about 7%, from about 0.4% to about6%, or from about 0.4% to about 5% and all ranges therebetween.

According to one embodiment, the coated article 100 may exhibit a singleside average light reflectance as measured at the anti-reflectivesurface 122 at the second portion 115 of the substrate 110 of about 8%or less, wherein the single side average light reflectance of the secondportion 115 is measured at a first incident illumination angle θ₂relative to n₂, and wherein the first incident illumination angle θ₂comprises an angle in the range from about 0 degrees to about 60 degreesfrom the n₂. In additional embodiments, the first incident illuminationangle θ₂ may comprise angles in the range from about 0 degrees to about60, from about 0 degrees to about 50, from about 0 degrees to about 40,from about 0 degrees to about 30, from about 0 degrees to about 20, orfrom about 0 degrees to about 10 from n₂. In additional embodiments, thecoated article 100 may exhibit a single side average light reflectanceas measured at the anti-reflective surface 122 at the second portion 115of the substrate 110 of about 8% or less for all incident illuminationangles θ₂ in a range from about 0 degrees to about 60 degrees, fromabout 0 degrees to about 50, from about 0 degrees to about 40, fromabout 0 degrees to about 30, from about 0 degrees to about 20, or fromabout 0 degrees to about 10 from n₂. In additional embodiments, givenany of the described ranges of incident illumination angles θ₂, thesingle side average light reflectance as measured at the anti-reflectivesurface 122 at the second portion 115 of the substrate 110 may be about10% or less, about 9% or less, about 8% or less, about 7% or less, about6% or less, about 5% or less, about 4% or less, about 3% or less, about2% or less, about 1% or less, or about 0.8% or less over the opticalwavelength regime. For example, the single side average lightreflectance may be in the range from about 0.4% to about 9%, from about0.4% to about 8%, from about 0.4% to about 7%, from about 0.4% to about6%, or from about 0.4% to about 5% and all ranges therebetween.

In another embodiment, the difference between the single side averagelight reflectance as measured at the anti-reflective surface 122 at thefirst portion 113 of the substrate 110, over any of the disclosedangular ranges, and the single side average light reflectance asmeasured at the anti-reflective surface 122 at the second portion 115 ofthe substrate 110, over any of the disclosed angular ranges, is 5% orless, 4% or less, 3% or less, 2% or less, or even 1% or less.

In another embodiment, the photopic reflectance at the first portion 113and/or the second portion 115 is in a range disclosed with regards tothe single-side average light reflectance over an angular rangedisclosed.

According to one embodiment, the coated article 100 may exhibit anaverage light transmittance as measured at the anti-reflective surface122 at the first portion 113 of the substrate 110 of about 8% or less,wherein the average light transmittance of the first portion 113 ismeasured at a first incident illumination angle θ₁ relative to n₁, andwherein the first incident illumination angle θ₁ comprises an angle inthe range from about 0 degrees to about 60 degrees from the n₁. Inadditional embodiments, the first incident illumination angle θ₁ maycomprise angles in the range from about 0 degrees to about 60, fromabout 0 degrees to about 50, from about 0 degrees to about 40, fromabout 0 degrees to about 30, from about 0 degrees to about 20, or fromabout 0 degrees to about 10 from n₁. In additional embodiments, thecoated article 100 may exhibit an average light transmittance asmeasured at the anti-reflective surface 122 at the first portion 113 ofthe substrate 110 of about 8% or less for all incident illuminationangles θ₁ in a range from about 0 degrees to about 60 degrees, fromabout 0 degrees to about 50, from about 0 degrees to about 40, fromabout 0 degrees to about 30, from about 0 degrees to about 20, or fromabout 0 degrees to about 10 from n₁. In additional embodiments, givenany of the described ranges of incident illumination angles θ₁, theaverage light transmittance as measured at the anti-reflective surface122 at the first portion 113 of the substrate 110 may be about 90% orgreater, 91% or greater, 92% or greater, 93% or greater, 94% or greater,95% or greater, 96% or greater, 97% or greater, or 98% or greater, overthe optical wavelength regime. For example, the average lighttransmittance may be in the range from about 90% to about 95.5%, fromabout 91% to about 95.5%, from about 92% to about 95.5%, from about 93%to about 95.5%, from about 94% to about 95.5%, from about 95% to about95.5%, from about 96% to about 95.5%, and all ranges therebetween.

According to one embodiment, the coated article 100 may exhibit anaverage light transmittance as measured at the anti-reflective surface122 at the second portion 115 of the substrate 110 of about 8% or less,wherein the average light transmittance of the second portion 115 ismeasured at a first incident illumination angle θ₂ relative to n₂, andwherein the first incident illumination angle θ₂ comprises an angle inthe range from about 0 degrees to about 60 degrees from the n₂. Inadditional embodiments, the first incident illumination angle θ₂ maycomprise angles in the range from about 0 degrees to about 60, fromabout 0 degrees to about 50, from about 0 degrees to about 40, fromabout 0 degrees to about 30, from about 0 degrees to about 20, or fromabout 0 degrees to about 10 from n₂. In additional embodiments, thecoated article 100 may exhibit an average light transmittance asmeasured at the anti-reflective surface 122 at the second portion 115 ofthe substrate 110 of about 8% or less for all incident illuminationangles θ₂ in a range from about 0 degrees to about 60 degrees, fromabout 0 degrees to about 50, from about 0 degrees to about 40, fromabout 0 degrees to about 30, from about 0 degrees to about 20, or fromabout 0 degrees to about 10 from n₂. In additional embodiments, givenany of the described ranges of incident illumination angles θ₂, theaverage light transmittance as measured at the anti-reflective surface122 at the second portion 115 of the substrate 110 may be about 90% orgreater, 91% or greater, 92% or greater, 93% or greater, 94% or greater,95% or greater, 96% or greater, 97% or greater, or 98% or greater, overthe optical wavelength regime. For example, the average lighttransmittance may be in the range from about 90% to about 95.5%, fromabout 91% to about 95.5%, from about 92% to about 95.5%, from about 93%to about 95.5%, from about 94% to about 95.5%, from about 95% to about95.5%, from about 96% to about 95.5%, and all ranges therebetween.

In another embodiment, the difference between the average lighttransmittance as measured at the anti-reflective surface 122 at thefirst portion 113 of the substrate 110, over any of the disclosedangular ranges, and the average light transmittance as measured at theanti-reflective surface 122 at the second portion 115 of the substrate110, over any of the disclosed angular ranges, is 5% or less, 4% orless, 3% or less, 2% or less, or even 1% or less.

In another embodiment, the photopic transmittance at the first portion113 and/or the second portion 115 is in a range disclosed with regardsto the average light transmittance over an angular range disclosed.

According to another embodiment, one or more of the single side averagelight reflectance, the average light transmittance, the photopicreflectance, the photopic transmittance, reflected color, andtransmitted color may be measured at the first portion 113 and at thesecond portion 115, wherein the first incident illumination angle θ₁comprises an angle in the range from about 0 degrees to about 60 degreesfrom n₁, the given optical at the second portion 115 is measured at asecond incident illumination angle θ₂, wherein the second incidentillumination angle θ₂ is in a direction equal to the direction v₁ of thefirst incident illumination angle such that the optical property at thefirst portion 113 and at the second portion 115 are measured in the sameviewing direction (i.e., v₁ is equal to v_(2,), but θ₁ is not equal toθ₂ because n₁ does not equal n₂).

Optical interference between reflected waves from the optical coating120/air interface and the optical coating 120/substrate 110 interfacecan lead to spectral reflectance and/or transmittance oscillations thatcreate apparent color in the coated article 100. In one or moreembodiments, the coated article 100 at the first portion 113 may exhibitan angular color shift in reflectance and/or transmittance of about 10or less when measured between normal n₁ to the viewing direction v₁ atthe incident illumination angle of θ₁. Additionally, in one or moreembodiments, the coated article 100 at the second portion 115 mayexhibit an angular color shift in reflectance and/or transmittance ofabout 10 or less when measured between normal n₂ to the viewingdirection v₂ at the incident illumination angle of θ₂.

According to one or more embodiments, the reference point color at thefirst portion 113 and at the second portion 115 may be less than about10 (such as about 9 or less, about 8 or less, about 7 or less, about 6or less, about 5 or less, about 4 or less, about 3 or less, or evenabout 2 or less). As used herein, the phrase “reference point color”refers to the a* and b*, under the CIE L*, a*, b* colorimetry system inreflectance and/or transmittance with respect to a reference color. Thereference color may be (a*,b*)=(0,0), (−2,−2), (−4,−4), or the colorcoordinates of the substrate 110. The reference point color may bemeasured at varying incident illumination angles θ₁ and θ₂. At (0,0)reference, the reference point color is defined as √(a*_(article))²+(b*article)²), at (−2,−2) reference, the reference point color is definedas √((a*_(article)+2)²+(b*_(article)+2)²), at (−4,−4) reference, thereference point color is defined as√((a*_(article)+4)²+(b*_(article)+4)²), at reference as the color of thesubstrate 110, the reference point color is defines as√((a*_(article)−a*_(substrate))²+(b*_(article)−b*_(substrate))²). Inembodiments, the reference point color may be measured at over angularranges, such that the incident illumination angles θ₁ and θ₂ maycomprise angles in the range from about 0 degrees to about 60, fromabout 0 degrees to about 50, from about 0 degrees to about 40, fromabout 0 degrees to about 30, from about 0 degrees to about 20, or fromabout 0 degrees to about 10 from n₁ or n₂. In another embodiment, forany of the disclosed incident illumination angle ranges, at the firstportion 113, and the second portion 115, or both, a* may be about 2 orless and b* may be about 2 or less.

As used herein, the phrase “angular color shift” refers to the change inboth a* and b*, under the CIE L*, a*, b* colorimetry system inreflectance and/or transmittance with shifting incident illuminationangles. It should be understood that unless otherwise noted, the L*coordinate of the articles described herein are the same at any angle orreference point and do not influence color shift. For example, angularcolor shift may be determined at a particular location of the coatedsubstrate 100 using the following equation:√((a* _(v) −a* _(n))²+(b* _(v) −b* _(n))²)with a*_(v), and b*_(v) representing the a* and b* coordinates of thearticle when viewed at incidence illumination angle and a*_(n), andb*_(n) representing the a* and b* coordinates of the article when viewedat or near normal.

In one or more embodiments, the angular color shift at the first portion113 may be about 10 or less, about 9 or less, about 8 or less, about 7or less, about 6 or less, about 5 or less, about 4 or less, about 3 orless, or even about 2 or less. Likewise, the angular color shift at thesecond portion 115 may be about 10 or less, about 9 or less, about 8 orless, about 7 or less, about 6 or less, about 5 or less, about 4 orless, about 3 or less, or even about 2 or less. The respective incidentillumination angles θ and θ₂ may comprise angles in the range from about0 degrees to about 60, from about 0 degrees to about 50, from about 0degrees to about 40, from about 0 degrees to about 30, from about 0degrees to about 20, or from about 0 degrees to about 10 from n₁ or n₂.In additional embodiments, the coated article 100 may a reflective ortransmittance color shift at the first portion 113 and at the secondportion 115 of the substrate 110 of about 10 or less for all incidentillumination angles θ in a range from about 0 degrees to about 60degrees, from about 0 degrees to about 50, from about 0 degrees to about40, from about 0 degrees to about 30, from about 0 degrees to about 20,or from about 0 degrees to about 10 from n₁. In some embodiments, theangular color shift may be about 0.

The illuminant can include standard illuminants as determined by theCIE, including A illuminants (representing tungsten-filament lighting),B illuminants (daylight simulating illuminants), C illuminants (daylightsimulating illuminants), D series illuminants (representing naturaldaylight), and F series illuminants (representing various types offluorescent lighting).

In another embodiment, the difference in reflected color of the coatedarticle 100 between the first portion 113 of the substrate 110 and thesecond portion 115 of the substrate 110 is less than or equal to about10 (such all about 9 or less, about 8 or less, about 7 or less, about 6or less, about 5 or less, about 4 or less, about 3 or less, about 2 orless, or even about 1 or less, wherein the difference in reflected coloris defined as:√((a* _(first portion) −a* _(second portion))²+(b* _(first portion) −b*_(second portion))²),and wherein the reflected color at the first portion 113 is measured ata first incident illumination angle θ₁ relative to n₁, and the reflectedcolor at the second portion 115 is measured at a second incidentillumination angle θ₂ measured relative to n₂. The respective incidentillumination angles θ₁ and θ₂ may comprise angles in the range fromabout 0 degrees to about 60, from about 0 degrees to about 50, fromabout 0 degrees to about 40, from about 0 degrees to about 30, fromabout 0 degrees to about 20, or from about 0 degrees to about 10 from n₁or n₂. In another embodiment, the difference in reflected color asdefined by√((a*_(first portion)−a*_(second portion))²+(b*_(first portion)−b*_(second portion))²)may be measured such that the second incident illumination angle θ₂ isin a direction equal to the direction v₁ of the first incidentillumination angle such that the optical property at the first portion113 and at the second portion 115 are measured in the same viewingdirection (i.e., v₁ is equal to v_(2,), but θ₁ is not equal to θ₂because n₁ does not equal n₂).

The substrate 110 may include an inorganic material and may include anamorphous substrate, a crystalline substrate, or a combination thereof.The substrate 110 may be formed from man-made materials and/or naturallyoccurring materials (e.g., quartz and polymers). For example, in someinstances, the substrate 110 may be characterized as organic and mayspecifically be polymeric. Examples of suitable polymers include,without limitation: thermoplastics including polystyrene (PS) (includingstyrene copolymers and blends), polycarbonate (PC) (including copolymersand blends), polyesters (including copolymers and blends, includingpolyethyleneterephthalate and polyethyleneterephthalate copolymers),polyolefins (PO) and cyclicpolyolefins (cyclic-PO), polyvinylchloride(PVC), acrylic polymers including polymethyl methacrylate (PMMA)(including copolymers and blends), thermoplastic urethanes (TPU),polyetherimide (PEI) and blends of these polymers with each other. Otherexemplary polymers include epoxy, styrenic, phenolic, melamine, andsilicone resins.

In some specific embodiments, the substrate 110 may specifically excludepolymeric, plastic and/or metal materials. The substrate 110 may becharacterized as alkali-including substrates (i.e., the substrateincludes one or more alkalis). In one or more embodiments, the substrate110 exhibits a refractive index in the range from about 1.45 to about1.55. In specific embodiments, the substrate 110 may exhibit an averagestrain-to-failure at a surface on one or more opposing major surfacesthat is 0.5% or greater, 0.6% or greater, 0.7% or greater, 0.8% orgreater, 0.9% or greater, 1% or greater, 1.1% or greater, 1.2% orgreater, 1.3% or greater, 1.4% or greater 1.5% or greater or even 2% orgreater, as measured using ball-on-ring testing using at least 5, atleast 10, at least 15, or at least 20 samples. In specific embodiments,the substrate 110 may exhibit an average strain-to-failure at itssurface on one or more opposing major surfaces of about 1.2%, about1.4%, about 1.6%, about 1.8%, about 2.2%, about 2.4%, about 2.6%, about2.8%, or about 3% or greater.

Suitable substrates 110 may exhibit an elastic modulus (or Young'smodulus) in the range from about 30 GPa to about 120 GPa. In someinstances, the elastic modulus of the substrate may be in the range fromabout 30 GPa to about 110 GPa, from about 30 GPa to about 100 GPa, fromabout 30 GPa to about 90 GPa, from about 30 GPa to about 80 GPa, fromabout 30 GPa to about 70 GPa, from about 40 GPa to about 120 GPa, fromabout 50 GPa to about 120 GPa, from about 60 GPa to about 120 GPa, fromabout 70 GPa to about 120 GPa, and all ranges and sub-rangestherebetween.

In one or more embodiments, the amorphous substrate may include glass,which may be strengthened or non-strengthened. Examples of suitableglass include soda lime glass, alkali aluminosilicate glass, alkalicontaining borosilicate glass and alkali aluminoborosilicate glass. Insome variants, the glass may be free of Lithia. In one or morealternative embodiments, the substrate 110 may include crystallinesubstrates such as glass ceramic substrates (which may be strengthenedor non-strengthened) or may include a single crystal structure, such assapphire. In one or more specific embodiments, the substrate 110includes an amorphous base (e.g., glass) and a crystalline cladding(e.g., sapphire layer, a polycrystalline alumina layer and/or or aspinel (MgAl₂O₄) layer).

The substrate 110 of one or more embodiments may have a hardness that isless than the hardness of the overall coated article 100 (as measured bythe Berkovich Indenter Hardness Test described herein). The hardness ofthe substrate 110 may be measured using known methods in the art,including but not limited to the Berkovich Indenter Hardness Test orVickers hardness test.

The substrate 110 may be substantially optically clear, transparent andfree from light scattering elements. In such embodiments, the substratemay exhibit an average light transmittance over the optical wavelengthregime of about 85% or greater, about 86% or greater, about 87% orgreater, about 88% or greater, about 89% or greater, about 90% orgreater, about 91% or greater, or about 92% or greater. In one or morealternative embodiments, the substrate 110 may be opaque or exhibit anaverage light transmittance over the optical wavelength regime of lessthan about 10%, less than about 9%, less than about 8%, less than about7%, less than about 6%, less than about 5%, less than about 4%, lessthan about 3%, less than about 2%, less than about 1%, or less thanabout 0.5%. In some embodiments, these light reflectance andtransmittance values may be a total reflectance or total transmittance(taking into account reflectance or transmittance on both major surfacesof the substrate) or may be observed on a single side of the substrate(i.e., on the anti-reflective surface 122 only, without taking intoaccount the opposite surface). Unless otherwise specified, the averagereflectance or transmittance of the substrate alone is measured at anincident illumination angle of 0 degrees relative to the substrate majorsurface 112 (however, such measurements may be provided at incidentillumination angles of 45 degrees or 60 degrees). The substrate 110 mayoptionally exhibit a color, such as white, black, red, blue, green,yellow, orange etc.

Additionally or alternatively, the physical thickness of the substrate110 may vary along one or more of its dimensions for aesthetic and/orfunctional reasons. For example, the edges of the substrate 110 may bethicker as compared to more central regions of the substrate 110. Thelength, width and physical thickness dimensions of the substrate 110 mayalso vary according to the application or use of the coated article 100.

The substrate 110 may be provided using a variety of differentprocesses. For instance, where the substrate 110 includes an amorphoussubstrate such as glass, various forming methods can include float glassprocesses and down-draw processes such as fusion draw and slot draw.

Once formed, a substrate 110 may be strengthened to form a strengthenedsubstrate. As used herein, the term “strengthened substrate” may referto a substrate that has been chemically strengthened, for examplethrough ion-exchange of larger ions for smaller ions in the surface ofthe substrate. However, other strengthening methods known in the art,such as thermal tempering, or utilizing a mismatch of the coefficient ofthermal expansion between portions of the substrate to createcompressive stress and central tension regions, may be utilized to formstrengthened substrates.

Where the substrate 110 is chemically strengthened by an ion exchangeprocess, the ions in the surface layer of the substrate are replacedby—or exchanged with—larger ions having the same valence or oxidationstate. Ion exchange processes are typically carried out by immersing asubstrate in a molten salt bath containing the larger ions to beexchanged with the smaller ions in the substrate. It will be appreciatedby those skilled in the art that parameters for the ion exchangeprocess, including, but not limited to, bath composition andtemperature, immersion time, the number of immersions of the substratein a salt bath (or baths), use of multiple salt baths, additional stepssuch as annealing, washing, and the like, are generally determined bythe composition of the substrate and the desired compressive stress(CS), depth of compressive stress layer (or depth of layer DOL, or depthof compression DOC) of the substrate that result from the strengtheningoperation. By way of example, ion exchange of alkali metal-containingglass substrates may be achieved by immersion in at least one moltenbath containing a salt such as, but not limited to, nitrates, sulfates,and chlorides of the larger alkali metal ion. The temperature of themolten salt bath typically is in a range from about 380° C. up to about450° C., while immersion times range from about 15 minutes up to about40 hours. However, temperatures and immersion times different from thosedescribed above may also be used.

In addition, non-limiting examples of ion exchange processes in whichglass substrates are immersed in multiple ion exchange baths, withwashing and/or annealing steps between immersions, are described in U.S.patent application Ser. No. 12/500,650, filed Jul. 10, 2009, by DouglasC. Allan et al., entitled “Glass with Compressive Surface for ConsumerApplications” and claiming priority from U.S. Provisional PatentApplication No. 61/079,995, filed Jul. 11, 2008, in which glasssubstrates are strengthened by immersion in multiple, successive, ionexchange treatments in salt baths of different concentrations; and U.S.Pat. No. 8,312,739, by Christopher M. Lee et al., issued on Nov. 20,2012, and entitled “Dual Stage Ion Exchange for Chemical Strengtheningof Glass,” and claiming priority from U.S. Provisional PatentApplication No. 61/084,398, filed Jul. 29, 2008, in which glasssubstrates are strengthened by ion exchange in a first bath is dilutedwith an effluent ion, followed by immersion in a second bath having asmaller concentration of the effluent ion than the first bath. Thecontents of U.S. patent application Ser. No. 12/500,650 and U.S. Pat.No. 8,312,739 are incorporated herein by reference in their entirety.

The degree of chemical strengthening achieved by ion exchange may bequantified based on the parameters of central tension (CT), surface CS,and depth of compression (DOC). Compressive stress (including surfaceCS) is measured by surface stress meter (FSM) using commerciallyavailable instruments such as the FSM-6000, manufactured by OriharaIndustrial Co., Ltd. (Japan). Surface stress measurements rely upon theaccurate measurement of the stress optical coefficient (SOC), which isrelated to the birefringence of the glass. SOC in turn is measuredaccording to Procedure C (Glass Disc Method) described in ASTM standardC770-16, entitled “Standard Test Method for Measurement of GlassStress-Optical Coefficient,” the contents of which are incorporatedherein by reference in their entirety. Maximum CT values are measuredusing a scattered light polariscope (SCALP) technique known in the art.As used herein, DOC means the depth at which the stress in thechemically strengthened alkali aluminosilicate glass article describedherein changes from compressive to tensile. DOC may be measured by FSMor SCALP depending on the ion exchange treatment. Where the stress inthe glass article is generated by exchanging potassium ions into theglass article, FSM is used to measure DOC. Where the stress is generatedby exchanging sodium ions into the glass article, SCALP is used tomeasure DOC. Where the stress in the glass article is generated byexchanging both potassium and sodium ions into the glass, the DOC ismeasured by SCALP, since it is believed the exchange depth of sodiumindicates the DOC and the exchange depth of potassium ions indicates achange in the magnitude of the compressive stress (but not the change instress from compressive to tensile); the exchange depth of potassiumions in such glass articles is measured by FSM.

In one embodiment, a substrate 110 can have a surface CS of 250 MPa orgreater, 300 MPa or greater, e.g., 400 MPa or greater, 450 MPa orgreater, 500 MPa or greater, 550 MPa or greater, 600 MPa or greater, 650MPa or greater, 700 MPa or greater, 750 MPa or greater or 800 MPa orgreater. The strengthened substrate may have a DOC (formerly DOL) of 10μm or greater, 15 μm or greater, 20 μm or greater (e.g., 25 μm, 30 μm,35 μm, 40 μm, 45 μm, 50 μm or greater) and/or a CT of 10 MPa or greater,20 MPa or greater, 30 MPa or greater, 40 MPa or greater (e.g., 42 MPa,45 MPa, or 50 MPa or greater) but less than 100 MPa (e.g., 95, 90, 85,80, 75, 70, 65, 60, 55 MPa or less). In one or more specificembodiments, the strengthened substrate has one or more of thefollowing: a surface CS greater than 500 MPa, a DOC (formerly DOL)greater than 15 μm, and a CT greater than 18 MPa.

Example glasses that may be used in the substrate 110 may include alkalialuminosilicate glass compositions or alkali aluminoborosilicate glasscompositions, though other glass compositions are contemplated. Suchglass compositions are capable of being chemically strengthened by anion exchange process. One example glass composition comprises SiO₂, B₂O₃and Na₂O, where (SiO₂+B₂O₃)≥66 mol. %, and Na₂O≥9 mol. %. In anembodiment, the glass composition includes at least 6 wt. % aluminumoxide. In a further embodiment, the substrate includes a glasscomposition with one or more alkaline earth oxides, such that a contentof alkaline earth oxides is at least 5 wt. %. Suitable glasscompositions, in some embodiments, further comprise at least one of K₂O,MgO, and CaO. In a particular embodiment, the glass compositions used inthe substrate can comprise 61-75 mol. % SiO2; 7-15 mol. % Al₂O₃; 0-12mol. % B₂O₃; 9-21 mol. % Na₂O; 0-4 mol. % K₂O; 0-7 mol. % MgO; and 0-3mol. % CaO.

A further example glass composition suitable for the substrate 110comprises: 60-70 mol. % SiO₂; 6-14 mol. % Al₂O₃; 0-15 mol. % B₂O₃; 0-15mol. % Li₂O; 0-20 mol. % Na₂O; 0-10 mol. % K₂O; 0-8 mol. % MgO; 0-10mol. % CaO; 0-5 mol. % ZrO₂; 0-1 mol. % SnO₂; 0-1 mol. % CeO₂; less than50 ppm As₂O₃; and less than 50 ppm Sb₂O₃; where 12 mol.%≤(Li₂O+Na₂O+K₂O)≤20 mol. % and 0 mol. %≤(MgO+CaO)≤10 mol. %.

A still further example glass composition suitable for the substrate 110comprises: 63.5-66.5 mol. % SiO₂; 8-12 mol. % Al₂O₃; 0-3 mol. % B₂O₃;0-5 mol. % Li₂O; 8-18 mol. % Na₂O; 0-5 mol. % K₂O; 1-7 mol. % MgO; 0-2.5mol. % CaO; 0-3 mol. % ZrO₂; 0.05-0.25 mol. % SnO₂; 0.05-0.5 mol. %CeO₂; less than 50 ppm As₂O₃; and less than 50 ppm Sb₂O₃; where 14 mol.%≤(Li₂O+Na₂O+K₂O)≤18 mol. % and 2 mol. %≤(MgO+CaO)≤7 mol. %.

In a particular embodiment, an alkali aluminosilicate glass compositionsuitable for the substrate 110 comprises alumina, at least one alkalimetal and, in some embodiments, greater than 50 mol. % SiO₂, in otherembodiments at least 58 mol. % SiO₂, and in still other embodiments atleast 60 mol. % SiO₂, wherein the ratio (Al₂O₃+B₂O₃)/Σmodifiers (i.e.,sum of modifiers) is greater than 1, where in the ratio the componentsare expressed in mol. % and the modifiers are alkali metal oxides. Thisglass composition, in particular embodiments, comprises: 58-72 mol. %SiO₂; 9-17 mol. % Al₂O₃; 2-12 mol. % B₂O₃; 8-16 mol. % Na₂O; and 0-4mol. % K₂O, wherein the ratio (Al₂O₃+B₂O₃)/Σmodifiers (i.e., sum ofmodifiers) is greater than 1.

In still another embodiment, the substrate 110 may include an alkalialuminosilicate glass composition comprising: 64-68 mol. % SiO₂; 12-16mol. % Na₂O; 8-12 mol. % Al₂O₃; 0-3 mol. % B₂O₃; 2-5 mol. % K₂O; 4-6mol. % MgO; and 0-5 mol. % CaO, wherein: 66 mol. %≤SiO₂+B₂O₃+CaO≤69 mol.%; Na₂O+K₂O+B₂O₃+MgO+CaO+SrO>10 mol. %; 5 mol. %≤MgO+CaO+SrO≤8 mol. %;(Na₂O+B₂O₃)−Al₂O₃≤2 mol. %; 2 mol. %≤Na₂O−Al₂O₃≤6 mol. %; and 4 mol.%≤(Na₂O+K₂O)−Al₂O₃≤10 mol. %.

In an alternative embodiment, the substrate 110 may comprise an alkalialuminosilicate glass composition comprising: 2 mol % or more of Al₂O₃and/or ZrO₂, or 4 mol % or more of Al₂O₃ and/or ZrO₂.

Where the substrate 110 includes a crystalline substrate, the substratemay include a single crystal, which may include Al₂O₃. Such singlecrystal substrates are referred to as sapphire. Other suitable materialsfor a crystalline substrate include polycrystalline alumina layer and/orspinel (MgAl₂O₄).

Optionally, the substrate 110 may be crystalline and include a glassceramic substrate, which may be strengthened or non-strengthened.Examples of suitable glass ceramics may include Li₂O—Al₂O₃—SiO₂ system(i.e. LAS-System) glass ceramics, MgO—Al₂O₃—SiO₂ system (i.e.MAS-System) glass ceramics, and/or glass ceramics that include apredominant crystal phase including β-quartz solid solution, β-spodumeness, cordierite, and lithium disilicate. The glass ceramic substrates maybe strengthened using the chemical strengthening processes disclosedherein. In one or more embodiments, MAS-System glass ceramic substratesmay be strengthened in Li₂SO₄ molten salt, whereby an exchange of 2Li⁺for Mg²⁺ can occur.

The substrate 110 according to one or more embodiments can have aphysical thickness ranging from about 100 μm to about 5 mm in variousportions of the substrate 110. Example substrate 110 physicalthicknesses range from about 100 μm to about 500 μm (e.g., 100, 200,300, 400 or 500 μm). Further example substrate 110 physical thicknessesrange from about 500 μm to about 1000 μm (e.g., 500, 600, 700, 800, 900or 1000 μm). The substrate 110 may have a physical thickness greaterthan about 1 mm (e.g., about 2, 3, 4, or 5 mm). In one or more specificembodiments, the substrate 110 may have a physical thickness of 2 mm orless, or less than 1 mm. The substrate 110 may be acid polished orotherwise treated to remove or reduce the effect of surface flaws.

The coated articles disclosed herein may be incorporated into anotherarticle such as an article with a display (or display articles) (e.g.,consumer electronics, including mobile phones, tablets, computers,navigation systems, and the like), architectural articles,transportation articles (e.g., automotive, trains, aircraft, sea craft,etc.), appliance articles, or any article that requires sometransparency, scratch-resistance, abrasion resistance or a combinationthereof. An exemplary article incorporating any of the coated articlesdisclosed herein is shown in FIGS. 43A and 43B. Specifically, FIGS. 43Aand 43B show a consumer electronic device 4100 including a housing 4102having front 4104, back 4106, and side surfaces 4108; electricalcomponents (not shown) that are at least partially inside or entirelywithin the housing and including at least a controller, a memory, and adisplay 4110 at or adjacent to the front surface of the housing; and acover substrate 4112 at or over the front surface of the housing suchthat it is over the display. In some embodiments, at least one of thecover substrate 4112 or a portion of housing 102 may include any of thecoated articles disclosed herein.

EXAMPLES

Various embodiments will be further clarified by the following examples.The optical properties of the examples were modeled using a computation.The computation was carried out using the thin-film design program“Essential Macleod” available from Thin Film Center, Inc. of TucsonAriz. The spectral transmittance was computed on a 1 nm interval for aselected wavelength range. Transmittance at each wavelength of a givencoated article was calculated based on inputted layer thicknesses andrefractive indices of each layer. Refractive index values for materialsof the coatings were experimentally derived or found in availableliterature. To experimentally determine the refractive index of amaterial, dispersion curves for the materials of the coating materialswere prepared. Layers of each coating material were formed onto siliconwafers by DC, RF or RF superimposed DC reactive sputtering from asilicon, aluminum, silicon and aluminum combined or co-sputtered, ormagnesium fluoride target (respectively) at a temperature of about 50°C. using ion assist. The wafer was heated to 200° C. during depositionof some layers and targets having a 3 inch diameter were used. Reactivegases used included nitrogen, fluorine and oxygen; argon was used as theinert gas. The RF power was supplied to the silicon target at 13.56 Mhzand DC power was supplied to the Si target, Al target and other targets.

The refractive indices (as a function of wavelength) of each of theformed layers and the glass substrate were measured using spectroscopicellipsometry. The refractive indices thus measured were then used tocalculate reflectance spectra for the examples. The examples use asingle refractive index value in their descriptive tables forconvenience, which corresponds to a point selected from the dispersioncurves at about 550 nm wavelength.

Comparative examples are supplied to compare the performance of coatingsdescribed herein with conventional coatings which may have inferioroptical performance when deposited on a non-planar substrate.

Comparative Example A

A planar glass substrate was coated with the coating of Table 1. FIG. 9depicts a graph of reflectance as a function of wavelength for theoptical coating of Table 1 with changing viewing angles relative to anormal angle of incidence. Line 202 corresponds to an angle of incidenceof 0 degrees, line 204 corresponds to an angle of incidence of 15degrees, line 206 corresponds to an angle of incidence of 30 degrees,line 208 corresponds to an angle of incidence of 45 degrees, line 210corresponds to an angle of incidence of 60 degrees. As can be seen fromFIG. 9 , as viewing angle was changed, reflectance (especially fromabout 650 nm and greater) increased. Therefore, this coating may haveobservable optical differences relative to different positions on asubstrate when coated on a non-planar substrate. Additionally, thecoating of Table 1 was modeled where each of its layers was thinned by ascalar of cosine of various deposition angles. For example, to model a15 degree deposition angle, each layer thickness was multiplied bycosine of 15 degrees. FIG. 10 depicts a graph of reflectance as afunction of wavelength for the optical coating of Table 1 with changinglayer thicknesses as observed at a normal viewing angle. Line 212corresponds to a 0 degrees deposition angle (identical to coating ofTable 1), line 214 corresponds to a 15 degrees deposition angle, line216 corresponds to a 30 degrees deposition angle, line 218 correspondsto a 45 degrees deposition angle, and line 220 corresponds to a 60degrees deposition angle. As is seen in FIG. 10 , reflectance increasedover portions of the visible spectrum when deposition angle wasincreased from 0 degrees.

TABLE 1 Material Refractive Index Thickness (nm) Glass 1.505 N/A SiNx1.878 9.6 SiO2 1.480 47.7 SiNx 1.878 28.4 SiO2 1.480 28.3 SiNx 1.87847.2 SiO2 1.480 8.3 SiNx 1.878 2000 SiO2 1.480 27.4 SiNx 1.878 29.7 SiO21.480 62.3 SiNx 1.878 30.8 SiO2 1.480 27.5 SiNx 1.878 105.8 SiO2 1.480 7SiNx 1.878 153.7 SiO2 1.480 87.1 air 1 N/A

Comparative Example B

A planar glass substrate was coated with the coating of Table 2. In FIG.11 , line 222 depicts a graph of reflectance as a function of wavelengthfor the optical coating of Comparative Example B (coating of Table 2) atan 8 degree viewing angle relative to normal.

TABLE 2 Material Refractive Index Thickness (nm) glass 1.505 N/A AlON2.006 8.2 SiO2 1.481 64.8 AlON 2.006 23 SiO2 1.481 47.8 AlON 2.006 39.3SiO2 1.481 25.5 AlON 2.006 42.85 SiO2 1.481 8.79 AlON 2.006 2000 SiO21.481 198.18 AlON 2.006 40.02 SiO2 1.481 41.36 AlON 2.006 44.79 SiO21.481 20.08 AlON 2.006 95.49 SiO2 1.481 10.2 AlON 2.006 158.86 SiO21.481 88.58 air 1 N/A

Example 1

A planar glass substrate was coated with the coating of Table 3. FIG. 11, line 224, depicts a graph of reflectance as a function of wavelengthfor the optical coating of Example 1 at an 8 degree viewing anglerelative to normal. As can be seen in FIG. 11 , the coating of Example 1had reduced first surface reflectance as compared to the coating ofComparative Example B at wavelengths over 700 nm.

TABLE 3 Thickness with Refractive Thickness 35 degree Material Index(nm) deposition angle glass 1.505 N/A N/A AlON 2.006 8.2 6.7 SiO2 1.48164.8 53.1 AlON 2.006 23 18.8 SiO2 1.481 47.8 39.2 AlON 2.006 39.3 32.2SiO2 1.481 25.5 20.9 AlON 2.006 54.5 44.6 SiO2 1.481 8 6.6 AlON 2.0062000 1638.3 SiO2 1.481 12.2 10.0 AlON 2.006 43.6 35.7 SiO2 1.481 40.333.0 AlON 2.006 22.4 18.3 SiO2 1.481 70 57.3 AlON 2.006 20 16.4 SiO21.481 39.4 32.3 AlON 2.006 137.4 112.6 SiO2 1.481 98.6 80.8 air 1 N/AN/A

FIG. 12 depicts a graph of reflectance as a function of wavelength forthe optical coating of Example 1 as designed and the optical coating ofExample 1 with reduced layer thickness representative of a depositionangle of 35 degrees, as viewed at a normal angle of incidence. As can beseen from FIG. 12 , the modeled deposition angle of 35 degrees causedincreased reflectance at wavelengths greater than about 700 nm. However,reflectance over the visible spectrum was relatively low.

FIG. 13 depicts a graph of a* versus b* in reflectance for L*a*b* colorspace for the optical coating of Example 1 as designed and with reducedlayer thickness representative of an increasing deposition angles, asviewed from a normal angle of incidence to 60 degrees.

The lines marked by 240 represent modeled deposition angles of 0 degreesto 30 degrees. There was little color change in the coating as a resultof deposition angle up to 30 degrees. Line 242 corresponds to adeposition angle of 35 degrees, line 244 corresponds to a depositionangle of 40 degrees, line 246 corresponds to a deposition angle of 45degrees, line 248 corresponds to a deposition angle of 50 degrees, line250 corresponds to a deposition angle of 55 degrees, and line 252corresponds to a deposition angle of 60 degrees. As modeled, b* is in arange of from 10 to 1 and a* is in a range from −5 to 0 for viewingangles of incidence of 0 degrees to 30 degrees. Also, b* is less than 2for deposition angles from 0 degrees to 40 degrees when viewed from 0degrees to 60 degrees.

Example 2

A planar glass substrate was coated with an optical coating having alower gradient layer, a scratch-resistant layer, and an upper gradientlayer. The lower gradient layer was formed on the glass substrate.Gradient layers were deposited in a Plasma-Therm Versaline HDPCVDchamber using SiO₂—SiON—SiN_(x) compositions deposited from silane,argon, oxygen, and nitrogen. Gradients were formed by breaking thetransition into a large number of short steps where the silane flow,oxygen, nitrogen, pressure, argon, coil RF power, and RF bias power arevaried between steps by a morph parameter where a morph parameter of 1was a linear curve while increasing above 1 formed an increasinglyconcave down curve and morph parameters below 1 formed increasinglyconcave up curves. The scratch-resistant layer was made of SiN_(x), andoxygen was added to achieve the gradient in the upper and lower gradientlayers.

FIG. 29 depicts the flow rates of N₂ (shown as reference number 306), O₂(shown as reference number 304), and SiH₄ (shown as reference number302) as a function of time that were utilized to deposit the coating.The deposition scheme of FIG. 29 was utilized to create an opticalcoating with a 500 nm lower gradient layer (morph=3), a 1800 nmscratch-resistant layer, and a 126 nm upper gradient layer. FIG. 30depicts the XPS composition profile formed by the conditions of FIG. 29, where reference number 308 represents nitrogen, reference number 310represents silicon, reference number 312 represents aluminum, referencenumber 314 represents oxygen, and reference number 316 representsfluorine. It should be noted that in FIG. 29 , the lower gradient layeris on the left-hand portion of the figure, and the upper gradient layeris on the right-hand side of the figure, whereas in FIG. 29 , the lowergradient layer is on the right-hand portion of the figure, and the uppergradient layer is on the left-hand side of the figure. FIG. 31 depictsthe calculated refractive index for the coating by the depositionconditions of FIG. 29 . The refractive index was calculated from MFCflows to a fit in index versus gas flows obtained from intermediatecompositions from the hard SiN_(x) layer to silica. It should beunderstood that the deposition as shown in FIG. 29 is the base case forExample 2, and if not specifically stated otherwise, when one parameterof the coating of Example 2 is modified, all other parameters are heldconsistent with the coating of FIG. 29 .

FIG. 14 depicts a graph of first surface reflectance for the opticalcoating of Example 2 (as deposited by the conditions of FIG. 29 ) forvarying viewing angles, where line 260 represents reflection at a 6degree angle of incidence, line 262 represents reflection at a 20 degreeangle of incidence, line 264 represents reflection at a 40 degree angleof incidence, and line 266 represents reflection at a 60 degree angle ofincidence. It can be observed that the gradient structure produces arelatively featureless reflectivity curve which looks very similar tobare glass in both intensity of reflectance and shape of thereflectivity as a function of wavelength. Also noted is the smallvariation of reflectivity as a function of viewing angle. Unlikenon-gradient dielectric stack designs, there is no shift in pass-band tochange color with viewing angle. The ˜2% ripple in the reflectance isbelieved to result from the step change in refractive index at thegradient/hard layer interfaces. This step change can be eliminated bymany methods, most obvious of which is additional oxygen mass flowcontrollers to span the range of flow required.

Samples were prepared with varying lower gradient layer thickness, wherethe scratch resistant layer was maintained at 1800 nm and the uppergradient layer was maintained at 126 nm. FIG. 32 depicts reflectance asa function of wavelength, where reference number 320 represents a 750 nmlower gradient layer, reference number 324 represents a 500 nm lowergradient layer, and reference number 322 represents a 250 nm lowergradient layer. Little change in reflectance or ripple is observedchanging the impedance match gradient thickness from 250 to 750 nm.

Optimum gradient structures typically use a quantic profile resembling asigmoid function. Sigmoid-like index profiles in the impedance matchgradient were generated by appending two power law gradients withinverse morph parameters. Samples were prepared with varying gradientcurves for a lower gradient layer of 500 nm. FIG. 33 shows reflectanceas a function of wavelength, where reference number 326 represents athird order polynomial fit gradient, reference number 324 represents a2-step sigmoid-like shape produced by appending the power law profilewith a second order curve, reference number 322 represents a 2-stepsigmoid-like shape produced by appending the power law profile with athird order curve, reference number 320 represents a 2-step sigmoid-likeshape produced by appending the power law profile with a fifth ordercurve. The various gradient shapes produces relatively similarreflectance.

FIG. 15 depicts a graph of a* versus b* of reflected D65 color in L*a*b*color space for the optical coatings of Example 2 having varying topgradient coating thicknesses at different viewing angles. The opencircles represent the samples having a 126 nm upper gradient layer, thesquares represent samples having a 256 nm upper gradient layer, and thetriangles represent samples having a 504 nm thickness. Each circle,triangle, or square represents a different viewing angle (i.e., 6degrees, 20 degrees, 40 degrees, or 60 degrees). FIG. 16 depicts a graphof a* versus b* of transmitted D65 color in L*a*b* color space for theoptical coatings of Example 2 having varying top gradient coatingthicknesses at a normal viewing angle. The “x” represent the sampleshaving a 126 nm upper gradient layer, the diamond represent sampleshaving a 256 nm upper gradient layer, and the square represent sampleshaving a 504 nm thickness. Thinner upper gradient layers resulted inmore color neutral coatings in several samples. FIGS. 34A and 34B showfirst surface reflectance color and transmission color, respectively,for varying gradient thickness. The overall variation in b* is largerthan a*. The most neutral color points are obtained with the thinner topcoating gradient layers.

FIGS. 35-38 depict the 1-surface reflected color, 2-surface reflectedcolor, modulus and hardness, and transmitted color as a function of topcoating gradient thickness, respectively. It can be seen that if atarget of −2≤a*≤0; −4≤b*≤0 for 1-surface reflectance, and −0.4≤a*≤0.4;0≤b*≤0.5 for transmittance is desired, a upper gradient layer thicknessof about 160-180 nm may achieve these optical parameters.

FIG. 17 shows calculated refractive index of the upper gradient layer asa function of thickness for a 126 nm thickness (reference number 274), a256 nm thickness (reference number 272), and a 504 nm thickness(reference number 270).

FIG. 18 depicts the Berkovich hardness profiles of samples prepared withvarying upper gradient layer thickness. Line 276 represents the hardnessprofile for a sample with a 126 nm upper gradient layer, line 278represents the hardness profile for a sample with a 256 nm uppergradient layer, and line 280 represents the hardness profile for asample with a 504 nm upper gradient layer. Thinner upper gradient layersresulted in increased hardness. Table 4 shows the modulus and hardnessas a function of changing upper gradient layer thickness.

TABLE 4 Upper gradient layer Thickness (nm) Modulus (GPa) Hardness (GPa)32 189 19.8 63 189 19.9 94 189 19.7 126 180 19.6 158 171 19.1 252 16418.4 504 153 17.5

Samples were produced with coatings described above with 126 nm uppergradient layers having varying morph parameters. FIG. 19 depicts a graphof the upper gradient layer profiles for the coating of Example 2 withvarying morph parameter, and FIG. 20 depicts the hardness profiles ofsamples prepared as Example 2 with varying upper gradient layer morphparameters. In FIGS. 19 and 20 , lines marked 282 represent a morphparameter of 0.2, lines marked 284 represent a morph parameter of 0.5,lines marked 286 represent a morph parameter of 0.3, lines marked 288represent a morph parameter of 0.5. Less linear morph parametersresulted generally in increased hardness. Table 5 shows the modulus andhardness as a function of changing morph parameter.

TABLE 5 Morph Max Berkovich parameter Modulus (GPa) Hardness (GPa) 0.2182 19.4 0.25 178 19.4 0.3 182 19.6 0.5 174 19

FIG. 21 depicts a graph of a* versus b* of reflected D65 color in L*a*b*color space for the optical coatings of Example 2 having varying topgradient morph parameters at different viewing angles, and FIG. 22depicts a graph of a* versus b* of transmitted D65 color in L*a*b* colorspace for the optical coatings of Example 2 having varying top gradientcoating morph parameters at a normal viewing angle, according to one ormore embodiments described herein. In FIG. 21 , the open circlesrepresent a morph parameter of 0.2, the squares represent a morphparameter of 0.25, the triangles represent a morph parameter of 0.3, andthe “x” represents a morph parameter of 0.5. In FIG. 22 , the “x”represents a morph parameter of 0.2, the diamond represents a morphparameter of 0.25, the square represents a morph parameter of 0.3, andthe triangle represents a morph parameter of 0.5.

FIG. 23 graphically depicts the average photopic transmittance and theaverage photopic reflection for the coatings of Example 2 having varyingupper gradient layer morph parameters, and FIG. 24 graphically depictsthe average photopic transmittance and the average photopic reflectionfor the coatings of Example 2 having varying upper gradient layerthicknesses. In both FIGS. 23 and 24 , squares represent averagephotopic reflectance over a 400 nm to 780 nm spectrum, and diamondsrepresent average photopic transmittance over a 400 nm to 780 nmspectrum. Additionally, FIG. 39 graphically depicts the hardness and2-surface photopic transmittance of the coatings of Example 2 as afunction of changing top gradient thickness. As shown in FIG. 39 ,certain embodiments have hardness of near 20 GPa (more than twice thatof some ion-exchanged glass substrates) while having photopictransmittance of over 90%, near that of bare glass.

Example 3

A coating was deposited onto a glass substrate which contained a sixlayer impedance match stack, a 2000 nm scratch-resistant coating, and a126 nm upper gradient layer. Thus, the coating of Example 3 was similarto that of Example 2 with the exception that the lower gradient layer ofExample 2 was replaced with a discrete layer stack in Example 3. Thecoating of Example 3 is shown in Table 6. The coating was deposited by asputtering technique.

TABLE 6 refractive index Material at 550 nm thickness (nm) Glass 1.505N/A SiAlON 2.007 6.8 SiO₂ 1.49 53.7 SiAlON 2.007 22.6 SiO₂ 1.49 29.6SiAlON 2.007 40.5 SiO₂ 1.49 8.5 SiAlON 2.007 2000 SiAlON → SiO₂ gradient126 air 1 N/A

FIG. 40 depicts the reflectance of the coating of Example 3 as afunction of wavelengths at varying viewing angles of incidence, wherereference number 354 represents a 6 degree angle of incidence, referencenumber 356 represents a 20 degree angle of incidence, reference number352 represents a 40 degree angle of incidence, and reference number 350represents a 60 degree angle of incidence. FIG. 42 shows the a* and b*first surface reflective color coordinates (as squares) for the coatedarticle of Example 34 at 6 degrees, 20 degrees, 40 degrees and 60degrees angle of incidence. The coated article of Example 3 had atransmitted color coordinate of about a*=−0.25 and b*=−0.25.

Example 4

A coating was deposited onto a glass substrate which contained a sixlayer impedance match stack, a 2000 nm scratch-resistant coating, and a126 nm upper gradient layer. Thus, the coating of Example 4 was similarto that of Example 2 with the exception that the lower gradient layer ofExample 2 was replaced with a discrete layer stack in Example 4.Additionally, the coating of Example 4 is similar to that of Example 3with the exception of the utilized coating materials. The coating ofExample 4 is shown in Table 7. The coating was deposited by PECVD.

TABLE 7 refractive index Material at 550 nm thickness (nm) Glass 1.505N/A SiN_(x) 1.878 6.8 SiO₂ 1.49 53.7 SiN_(x) 1.878 22.6 SiO₂ 1.49 29.6SiN_(x) 1.878 40.5 SiO₂ 1.49 8.5 SiN_(x) 1.878 2000 SiN_(x) → SiO₂gradient 126 air 1 N/A

FIG. 41 depicts the reflectance of the coating of Example 4 as afunction of wavelengths at varying viewing angles of incidence, wherereference number 360 represents a 6 degree angle of incidence, referencenumber 362 represents a 20 degree angle of incidence, reference number364 represents a 40 degree angle of incidence, and reference number 366represents a 60 degree angle of incidence. FIG. 42 shows the a* and b*first surface color coordinates (as diamonds) for the coated article ofExample 4 at 6 degrees, 20 degrees, 40 degrees and 60 degrees angle ofincidence. The coated article of Example 4 had a transmitted colorcoordinate of about a*=−0.2 and b*=0.7.

Table 8 reports hardness, modulus, photopic transmittance, and photopicreflectance for the coated articles of three sample coatings. SampleCoatings A and B have a conventional 6-layer impedance match stack, 2micron hard coating, and ˜125 nm thick AR gradient. Coating sample A wasdeposited by CVD on the Plasma-Therm HDPCVD with SiO2-SiON—SiNx materialsystem. Coating sample B was deposited by sputtering on the AJA usingSiAlON—SiO2 material system. Coating sample C has a 250 nm thickimpedance match gradient, 2 um hard coating, and 125 nm thick ARgradient. was deposited by CVD on the Plasma-Therm HDPCVD withSiO2-SiON—SiNx material system. Performance was nearly identical.

TABLE 8 Coating Sample E(GPa) H(GPa) T(%) R(%) A 180 19 0.914 0/081 B206 18.9 0.919 0.777 C 176 19.4 0.918 0.079

The various features described in the specification may be combined inany and all combinations, for example, as listed in the followingembodiments.

Embodiment 1. A Coated Article Comprising:

a substrate having a major surface, the major surface comprising a firstportion and a second portion, wherein a first direction that is normalto the first portion of the major surface is not equal to a seconddirection that is normal to the second portion of the major surface, andthe angle between the first direction and the second direction is in arange of from about 10 degrees to about 180 degrees; and

an optical coating disposed on at least the first portion and the secondportion of the major surface, the optical coating forming ananti-reflective surface, wherein:

the coated article exhibits at the first portion of the substrate and atthe second portion of the substrate hardness of about 8 GPa or greaterat an indentation depth of about 50 nm or greater as measured on theanti-reflective surface by a Berkovich Indenter Hardness Test;

the coated article exhibits a single side average light reflectance asmeasured at the anti-reflective surface at the first portion of thesubstrate of about 8% or less, wherein the single side average lightreflectance of the first portion is measured at a first incidentillumination angle relative to the first direction, wherein the firstincident illumination angle comprises an angle in the range from about 0degrees to about 60 degrees from the first direction;

the coated article exhibits a single-side average light reflectance asmeasured at the anti-reflective surface at the second portion of thesubstrate of about 8% or less, wherein the single side average lightreflectance of the second portion is measured at a second incidentillumination angle relative to the second direction, wherein the secondincident illumination angle comprises an angle in the range from about 0degrees to about 60 degrees from the second direction; and

the single side average light reflectance at the first portion and atthe second portion is measured over an optical wavelength regime in arange of from about 400 nm to about 800 nm.

Embodiment 2. The coated article of embodiment 1, wherein the anglebetween the first direction normal to the first portion and the seconddirection normal to the second portion is in a range of from about 10degrees to about 90 degrees.

Embodiment 3. The coated article of embodiment 1 or embodiment 2,wherein:

the first incident illumination angle comprises an angle in the rangefrom about 0 degrees to about 10 degrees from the first direction; and

the second incident illumination angle comprises an angle in a rangefrom about 0 degrees to about 10 degrees from the second direction.

Embodiment 4. The coated article of any one of embodiments 1-3, wherein:

the coated article exhibits a single side average light reflectance asmeasured at the anti-reflective surface at the first portion of thesubstrate of about 8% or less for all angles in the range from about 0degrees to about 60 degrees; and

the coated article exhibits a single-side average light reflectance asmeasured at the anti-reflective surface at the second portion of thesubstrate of about 8% or less for all angles in the range from about 0degrees to about 60 degrees.

Embodiment 5. The coated article of any one of embodiments 1-4, whereinthe coated article exhibits a single side average light reflectance asmeasured at the anti-reflective surface at the first portion of thesubstrate of about 5% or less; and

the coated article exhibits a single-side average light reflectance asmeasured at the anti-reflective surface at the second portion of thesubstrate of about 5% or less.

Embodiment 6. A coated article comprising:

a substrate having a major surface, the major surface comprising a firstportion and a second portion, wherein a first direction that is normalto the first portion of the major surface is not equal to a seconddirection that is normal to the second portion of the major surface, andthe angle between the first direction and the second direction is in arange of from about 10 degrees to about 180 degrees; and

an optical coating disposed on at least the first portion and the secondportion of the major surface, the optical coating forming ananti-reflective surface, wherein:

the coated article exhibits at the first portion of the substrate and atthe second portion of the substrate hardness of about 8 GPa or greaterat an indentation depth of about 50 nm or greater as measured on theanti-reflective surface by a Berkovich Indenter Hardness Test; and

the difference in reflected color of the coated article between thefirst portion of the substrate and the second portion of the substrateis less than or equal to about 10 as measured by the reflectance colorcoordinates in the (L*, a*, b*) colorimetry system under anInternational Commission on Illumination illuminant, wherein thedifference in reflected color is defined as √((a*first portion−a*secondportion)2+(b*first portion−b*second portion)2), and wherein thereflected color at the first portion is measured at a first incidentillumination angle relative to the first direction, wherein the firstincident illumination angle comprises an angle in the range from about 0degrees to about 60 degrees from the first direction, and the reflectedcolor at the second portion is measured at a second incidentillumination angle relative to the second direction, wherein the secondincident illumination angle comprises an angle in a range from about 0degrees to about 60 degrees from the second direction.

Embodiment 7. The coated article of embodiment 6, wherein the differencein reflected color of the coated article between the first portion ofthe substrate and the second portion of the substrate is less than orequal to about 5.

Embodiment 8. The coated article of embodiment 6 or embodiment 7,wherein the angle between the first direction and the second directionis in a range of from about 10 degrees to about 90 degrees

Embodiment 9. The coated article of any one of embodiments 6-8, wherein:

the first incident illumination angle comprises an angle in the rangefrom about 0 degrees to about 10 degrees from the first direction; and

the second incident illumination angle comprises an angle in a rangefrom about 0 degrees to about 10 degrees from the second direction.

Embodiment 10. The coated article of any one of embodiments 6-9, whereinthe difference in reflected color of the coated article between thefirst portion of the substrate and the second portion of the substrateis less than or equal to about 10 for all first incident illuminationangles in the range from about 0 degrees to 60 degrees and for allsecond incident illumination angles in the range from about 0 degrees toabout 60 degrees.

Embodiment 11. The coated article of any one of embodiments 6-10,wherein the reference point color at the first portion is about 10 orless and the reference point color at the second portion is about 10 orless, wherein the reference point color at the first portion is measuredat the first incident illumination angle and at the second portion ismeasured at the second incident illumination angle, and wherein thereference point is (a*,b*)=(0,0), (−2,−2), or (−4,−4).

Embodiment 12. The coated article of any one of embodiments 6-10,wherein the reference point color at the first portion is about 5 orless and the reference point color at the second portion is about 5 orless, wherein the reference point color at the first portion is measuredat the first incident illumination angle and at the second portion ismeasured at the second incident illumination angle, and wherein thereference point is (a*,b*)=(0,0), (−2,−2), or (−4,−4).

Embodiment 13. A coated article comprising:

a substrate having a major surface, the major surface comprising a firstportion and a second portion, wherein a first direction that is normalto the first portion of the major surface is not equal to a seconddirection that is normal to the second portion of the major surface, andthe angle between the first direction and the second direction is in arange of from about 10 degrees to about 180 degrees; and

an optical coating disposed on at least the first portion and the secondportion of the major surface, the optical coating forming ananti-reflective surface, wherein:

the coated article exhibits at the first portion of the substrate and atthe second portion of the substrate hardness of about 8 GPa or greaterat an indentation depth of about 50 nm or greater as measured on theanti-reflective surface by a Berkovich Indenter Hardness Test; and

the difference in reflected color of the coated article between thefirst portion of the substrate and the second portion of the substrateis less than or equal to about 10 as measured by the reflectance colorcoordinates in the (L*, a*, b*) colorimetry system under anInternational Commission on Illumination illuminant, wherein thedifference in reflected color is defined as √((a*first portion−a*secondportion)2+(b*first portion−b*second portion)2), and wherein thereflected color at the first portion is measured at a first incidentillumination angle relative to the first direction, wherein the firstincident illumination angle comprises an angle in the range from about 0degrees to about 60 degrees from the first direction, and the reflectedcolor at the second portion is measured at a second incidentillumination angle, wherein the second incident illumination angle is ina direction equal to the direction of the first incident illuminationangle such that the reflected color at the first portion and at thesecond portion are measured in the same viewing direction.

Embodiment 14. The coated article of any of embodiments 1-13, whereinthe first incident illumination angle comprises an angle in the rangefrom about 0 degrees to 10 degrees from the first direction.

Embodiment 15. The coated article of any of embodiments 1-14, whereinthe substrate comprises an amorphous substrate or a crystallinesubstrate.

Embodiment 16. The coated article of any of embodiments 1-15, whereinthe optical coating comprises a first gradient layer in contact with thesubstrate, a scratch-resistant layer over the first gradient layer, anda second gradient layer over the scratch-resistant layer which definesthe anti-reflective surface, wherein:

the refractive index of the first gradient layer at the substrate iswithin 0.2 of the refractive index of the substrate;

the refractive index of the first gradient layer at thescratch-resistant layer is within 0.2 of the refractive index of thescratch-resistant layer;

the refractive index of the second gradient layer at thescratch-resistant layer is within 0.2 of the refractive index of thescratch-resistant layer; and

the refractive index of the second gradient layer at the anti-reflectivesurface is from about 1.35 to about 1.7.

Embodiment 17. The coated article of any of embodiments 1-15, whereinthe optical coating comprises a first anti-reflective coating, ascratch-resistant layer over the first anti-reflective coating, and asecond anti-reflective coating over the scratch-resistant layer whichdefines the anti-reflective surface, wherein the first anti-reflectivecoating comprises at least a low RI layer and a high RI layer, and thesecond anti-reflective coating comprises at least a low RI layer and ahigh RI layer.

Embodiment 18. The coated article of any of embodiments 1-15, whereinthe optical coating comprises a gradient layer in contact with thesubstrate, a scratch-resistant layer over the gradient layer, and ananti-reflective coating over the scratch-resistant layer which definesthe anti-reflective surface, wherein:

the refractive index of the gradient layer at the substrate is within0.2 of the refractive index of the substrate;

the refractive index of the gradient layer at the scratch-resistantlayer is within 0.2 of the refractive index of the scratch-resistantlayer; and

the anti-reflective coating comprises at least a low RI layer and a highRI layer.

Embodiment 19. The coated article of any of embodiments 1-15, whereinthe optical coating comprises an anti-reflective coating in contact withthe substrate, a scratch-resistant layer over the anti-reflectivecoating, and a gradient layer over the scratch-resistant layer whichdefines the anti-reflective surface, wherein:

the anti-reflective coating comprises at least a low RI layer and a highRI layer;

the refractive index of the anti-reflective coating at thescratch-resistant layer is within 0.2 of the refractive index of thescratch-resistant layer; and

the refractive index of the gradient layer at the anti-reflectivesurface is from about 1.35 to about 1.7.

What is claimed is:
 1. A coated article comprising: a substrate having amajor surface, the major surface comprising a first portion and a secondportion, wherein a first direction that is normal to the first portionof the major surface is not equal to a second direction that is normalto the second portion of the major surface, and the angle between thefirst direction and the second direction is in a range of from about 10degrees to about 180 degrees; and an optical coating disposed on atleast the first portion and the second portion of the major surface, theoptical coating forming an anti-reflective surface, wherein: the coatedarticle exhibits at the first portion of the major surface and at thesecond portion of the major surface a hardness of about 8 GPa orgreater; the coated article exhibits a photopic reflectance as measuredat the anti-reflective surface at the first portion of the major surfaceof about 2% or less, wherein the photopic reflectance of the firstportion is measured at a first incident illumination angle relative tothe first direction, wherein the first incident illumination anglecomprises an angle in a range from about 0 degrees to about 60 degreesfrom the first direction; the coated article exhibits a photopicreflectance as measured at the anti-reflective surface at the secondportion of the major surface of about 2% or less, wherein the photopicreflectance of the second portion is measured at a second incidentillumination angle relative to the second direction, wherein the secondincident illumination angle comprises an angle in a range from about 0degrees to ab out 60 degrees from the second direction; the photopicreflectance at the first portion and at the second portion is measuredover an optical wavelength regime in a range of from about 400 nm to about 800 nm; and wherein: the first incident illumination angle comprisesan angle in a range from about 0 degrees to about 10 degrees from thefirst direction; and the second incident illumination angle comprises anangle in a range from about 0 degrees to about 10 degrees from thesecond direction.
 2. The coated article of claim 1, further comprising:a difference in reflected color of the coated article between the firstportion of the major surface and the second portion of the major surfaceis less than or equal to about 5 as measured by the reflectance colorcoordinates in the (L*, a*, b*) colorimetry system under anInternational Commission on Illumination illuminant, wherein thedifference in reflected color is defined as√((a*_(first portion)−a*_(second portion))²+(b*_(first portion)−b*_(second portion))²),and wherein the reflected color at the first portion is measured at afirst incident illumination angle relative to the first direction,wherein the first incident illumination angle comprises an angle in arange from about 0 degrees to about 60 degrees from the first direction,and the reflected color at the second portion is measured at a secondincident illumination angle, wherein the second incident illuminationangle is in a direction equal to the direction of the first incidentillumination angle such that the reflected color at the first portionand at the second portion are measured in the same viewing direction. 3.The coated article of claim 1, wherein the angle between the firstdirection and the second direction is in a range of from about 30degrees to ab out 180 degrees.
 4. The coated article of claim 1, whereinthe angle between the first direction and the second direction is in arange of from about 40 degrees to ab out 180 degrees.
 5. The coatedarticle of claim 1, wherein the angle between the first direction andthe second direction is in a range of from about 50 degrees to ab out180 degrees.
 6. The coated article of claim 1, wherein: the photopicreflectance as measured at the anti-reflective surface at the firstportion of the major surface is about 1% or less; and, the photopicreflectance as measured at the anti-reflective surface at the secondportion of the major surface is about 1% or less.
 7. The coated articleof claim 6, further comprising: a difference in reflected color of thecoated article between the first portion of the major surface and thesecond portion of the major surface is less than or equal to about 3 asmeasured by the reflectance color coordinates in the (L*, a*, b*)colorimetry system under an International Commission on Illuminationilluminant, wherein the difference in reflected color is defined as√((a*_(first portion)−a*_(second portion))²+(b*_(first portion)−b*_(second portion))²),and wherein the reflected color at the first portion is measured at afirst incident illumination angle relative to the first direction,wherein the first incident illumination angle comprises an angle in arange from about 0 degrees to about 60 degrees from the first direction,and the reflected color at the second portion is measured at a secondincident illumination angle relative to the second direction, whereinthe second incident illumination angle comprises an angle in a rangefrom about 0 degrees to about 60 degrees from the second direction. 8.The coated article of claim 6, further comprising: a difference inreflected color of the coated article between the first portion of themajor surface and the second portion of the major surface is less thanor equal to about 3 as measured by the reflectance color coordinates inthe (L*, a*, b*) colorimetry system under an International Commission onIllumination illuminant, wherein the difference in reflected color isdefined as√((a*_(first portion)−a*_(second portion))²+(b*_(first portion)−b*_(second portion))²),and wherein the reflected color at the first portion is measured at afirst incident illumination angle relative to the first direction,wherein the first incident illumination angle comprises an angle in arange from about 0 degrees to about 60 degrees from the first direction,and the reflected color at the second portion is measured at a secondincident illumination angle, wherein the second incident illuminationangle is in a direction equal to the direction of the first incidentillumination angle such that the reflected color at the first portionand at the second portion are measured in the same viewing direction. 9.The coated article of claim 1, wherein the optical coating comprises afirst anti-reflective coating, a scratch-resistant layer over the firstanti-reflective coating, and a second anti-reflective coating over thescratch-resistant layer which defines the anti-reflective surface,wherein the first anti-reflective coating comprises at least a low RIlayer and a high RI layer, and the second anti-reflective coatingcomprises at least a low RI layer and a high RI layer.
 10. The coatedarticle of claim 9, wherein the total thickness of the optical coatingis from about 1 μm to about 5 μm, wherein the total thickness of thefirst anti-reflective coating and the second anti-reflective coating isfrom about 200 nm to about 800 nm, and further wherein the opticalcoating comprises a capping layer over the second anti-reflectivecoating, the capping layer comprising a low RI material.
 11. The coatedarticle of claim 9, wherein the total thickness of the at least a low RIlayer in the second anti-reflective coating is less than 500 nm, andwherein the total thickness of the at least a high RI layer in the firstand the second anti-reflective coating is about 200 nm or greater, andfurther wherein the total thickness of the second anti-reflectivecoating is less than or equal to about 1000 nm.
 12. The coated articleof claim 9, wherein the at least a low RI layer in each of the first andthe second anti-reflective coatings comprises silicon oxide, wherein theat least a high RI layer in the first anti-reflective coating comprisessilicon oxynitride, wherein the at least a high RI layer in the secondanti-reflective coating comprises silicon nitride, and further whereinthe scratch-resistant layer comprises silicon oxynitride.
 13. The coatedarticle of claim 9, wherein the coated article exhibits a photopicreflectance as measured at the anti-reflective surface at the firstportion of the major surface of about 2% or less, wherein the photopicreflectance of the first portion is measured at a first incidentillumination angle relative to the first direction, wherein the firstincident illumination angle comprises an angle in a range from about 0degrees to about 60 degrees from the first direction.
 14. A coatedarticle comprising: a substrate having a major surface, the majorsurface comprising a first portion and a second portion, wherein a firstdirection that is normal to the first portion of the major surface isnot equal to a second direction that is normal to the second portion ofthe major surface, and the angle between the first direction and thesecond direction is in a range of from about 10 degrees to about 180degrees; and an optical coating disposed on at least the first portionand the second portion of the major surface, the optical coating formingan anti-reflective surface, wherein: the coated article exhibits at thefirst portion of the major surface and at the second portion of themajor surface a hardness of about 8 GPa or greater; the coated articleexhibits a photopic reflectance as measured at the anti-reflectivesurface at the first portion of the major surface of about 2% or less,wherein the photopic reflectance of the first portion is measured at afirst incident illuminati on angle relative to the first direction,wherein the first incident illumination angle comprises an angle in arange from about 0 degrees to about 60 degrees from the first direction;the coated article exhibits a photopic reflectance as measured at theanti-reflective surface at the second portion of the major surface ofabout 2% or less, wherein the photopic reflectance of the second portionis measured at a second incident illumination angle relative to thesecond direction, wherein the second incident illumination anglecomprises an angle in a range from about 0 degrees to about 60 degreesfrom the second direction; the photopic reflectance at the first portionand at the second portion is measured over an optical wavelength regimein a range of from about 400 nm to about 800 nm; and the coated articlefurther comprising: a difference in reflected color of the coatedarticle between the first portion of the major surface and the secondportion of the major surface is less than or equal to about 5 asmeasured by the reflectance color coordinates in the (L*, a*, b*)colorimetry system under an International Commission on Illuminationilluminant, wherein the difference in reflected color is defined as√((a*_(first portion)−a*_(second portion))²+(b*_(first portion)−b*_(second portion))²),and wherein the reflected color at the first portion is measured at afirst incident illumination angle relative to the first direction,wherein the first incident illumination angle comprises an angle in arange from about 0 degrees to about 60 degrees from the first direction,and the reflected color at the second portion is measured at a secondincident illumination angle relative to the second direction, whereinthe second incident illumination angle comprises an angle in a rangefrom about 0 degrees to about 60 degrees from the second direction. 15.A coated article comprising: a substrate having a major surface, themajor surface comprising a first portion and a second portion, wherein afirst direction that is normal to the first portion of the major surfaceis not equal to a second direction that is normal to the second portionof the major surface, and the angle between the first direction and thesecond direction is in a range of from about 10 degrees to about 180degrees; and an optical coating disposed on at least the first portionand the second portion of the major surface, the optical coating formingan anti-reflective surface, wherein: the coated article exhibits at thefirst portion of the major surface and at the second portion of themajor surface a hardness of about 8 GPa or greater; the coated articleexhibits a photopic reflectance as measured at the anti-reflectivesurface at the first portion of the major surface of about 2% or less,wherein the photopic reflectance of the first portion is measured at afirst incident illuminati on angle relative to the first direction,wherein the first incident illumination angle comprises an angle in arange from about 0 degrees to about 60 degrees from the first direction;the coated article exhibits a photopic reflectance as measured at theanti-reflective surface at the second portion of the major surface ofabout 2% or less, wherein the photopic reflectance of the second portionis measured at a second incident illumination angle relative to thesecond direction, wherein the second incident illumination anglecomprises an angle in a range from about 0 degrees to about 60 degreesfrom the second direction; the photopic reflectance at the first portionand at the second portion is measured over an optical wavelength regimein a range of from about 400 nm to about 800 nm; and the optical coatingcomprises a first gradient layer in contact with the substrate, ascratch-resistant layer over the first gradient layer, and a secondgradient layer over the scratch-resistant layer which defines theanti-reflective surface, wherein: the refractive index of the firstgradient layer at the substrate is within 0.2 of the refractive index ofthe substrate; the refractive index of the first gradient layer at thescratch-resistant layer is within 0.2 of the refractive index of thescratch-resistant layer; the refractive index of the second gradientlayer at the scratch-resistant layer is within 0.2 of the refractiveindex of the scratch-resistant layer; and the refractive index of thesecond gradient layer at the anti-reflective surface is from about 1.35to about 1.7.
 16. A coated article comprising: a substrate having amajor surface, the major surface comprising a first portion and a secondportion, wherein a first direction that is normal to the first portionof the major surface is not equal to a second direction that is normalto the second portion of the major surface, and the angle between thefirst direction and the second direction is in a range of from about 10degrees to about 180 degrees; and an optical coating disposed on atleast the first portion and the second portion of the major surface, theoptical coating forming an anti-reflective surface, wherein: the coatedarticle exhibits at the first portion of the major surface and at thesecond portion of the major surface a hardness of about 8 GPa orgreater; the coated article exhibits a photopic reflectance as measuredat the anti-reflective surface at the first portion of the major surfaceof about 2% or less, wherein the photopic reflectance of the firstportion is measured at a first incident illumination angle relative tothe first direction, wherein the first incident illumination anglecomprises an angle in a range from about 0 degrees to about 60 degreesfrom the first direction; the coated article exhibits a photopicreflectance as measured at the anti-reflective surface at the secondportion of the major surface of about 2% or less, wherein the photopicreflectance of the second portion is measured at a second incidentillumination angle relative to the second direction, wherein the secondincident illumination angle comprises an angle in a range from about 0degrees to about 60 degrees from the second direction; the photopicreflectance at the first portion and at the second portion is measuredover an optical wavelength regime in a range of from about 400 nm toabout 800 nm; and the optical coating comprises a gradient layer incontact with the substrate, a scratch-resistant layer over the gradientlayer, and an anti-reflective coating over the scratch-resistant layerwhich defines the anti-reflective surface, wherein: the refractive indexof the gradient layer at the substrate is within 0.2 of the refractiveindex of the substrate; the refractive index of the gradient layer atthe scratch-resistant layer is within 0.2 of the refractive index of thescratch-resistant layer; and the anti-reflective coating comprises atleast a low RI layer and a high RI layer.
 17. A coated articlecomprising: a substrate having a major surface, the major surfacecomprising a first portion and a second portion, wherein a firstdirection that is normal to the first portion of the major surface isnot equal to a second direction that is normal to the second portion ofthe major surface, and the angle between the first direction and thesecond direction is in a range of from about 10 degrees to about 180degrees; and an optical coating disposed on at least the first portionand the second portion of the major surface, the optical coating formingan anti-reflective surface, wherein: the coated article exhibits at thefirst portion of the major surface and at the second portion of themajor surface a hardness of about 8 GPa or greater; the coated articleexhibits a photopic reflectance as measured at the anti-reflectivesurface at the first portion of the major surface of about 2% or less,wherein the photopic reflectance of the first portion is measured at afirst incident illuminati on angle relative to the first direction,wherein the first incident illumination angle comprises an angle in arange from about 0 degrees to about 60 degrees from the first direction;the coated article exhibits a photopic reflectance as measured at theanti-reflective surface at the second portion of the major surface ofabout 2% or less, wherein the photopic reflectance of the second portionis measured at a second incident illumination angle relative to thesecond direction, wherein the second incident illumination anglecomprises an angle in a range from about 0 degrees to about 60 degreesfrom the second direction; the photopic reflectance at the first portionand at the second portion is measured over an optical wavelength regimein a range of from about 400 nm to about 800 nm; and the optical coatingcomprises an anti-reflective coating in contact with the substrate, ascratch-resistant layer over the anti-reflective coating, and a gradientlayer over the scratch-resistant layer which defines the anti-reflectivesurface, wherein: the anti-reflective coating comprises at least a lowRI layer and a high RI layer; the refractive index of theanti-reflective coating at the scratch-resistant layer is within 0.2 ofthe refractive index of the scratch-resistant layer; and the refractiveindex of the gradient layer at the anti-reflective surface is from about1.35 to about 1.7.
 18. A consumer electronic product, comprising: ahousing having a front surface, a back surface and side surfaces;electrical components at least partially within the housing, theelectrical components including at least a controller, a memory, and adisplay, the display at or adjacent the front surface of the housing;and a cover substrate disposed over the display, wherein at least one ofa portion of the housing or the cover substrate comprises the coatedarticle of claim 1.